Wednesday, December 4, 2013

Stanford University Seminar - On The Origin Of Experience

The full transcript of this lecture, including the first chapter of "On The Origin Of Experience: The Shaping Of Sense And The Complex World," is available here.

The preview is not a permanent document, so please do not cite it. It you must cite something immediately then you may refer to the Stanford University lecture directly, since that will have some permanence. Subject to Steven's health and well-being the book will be published in the February/March timeframe. And the citation will look something like this:

Ericsson-Zenith, Steven. On The Origin Of Experience : The Shaping Of Sense And The Complex World. Institute for Advanced Science & Engineering (Publications). ISBN XXXXXXXXXX. 2017.

Thursday, October 10, 2013

On The Origin Of Experience (Volume One)

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: 


Steven Ericsson-Zenith

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.

Tuesday, September 24, 2013

Events, 2013/2014

Steven has been invited to lecture at Stanford University in the EE380 Fall and Winter quarters. Both events will be recorded and subsequently available via Stanford's presence on iTunesU and YouTube.

Nov. 13th (Fall Quarter): 
On The Origin Of Experience: 
The Shaping Of Sense And The Complex World.

This Fall lecture will introduce Steven's new book.

Jan 15th (Winter Quarter): 
Charles Sanders Peirce (1839-1914): 
His life and contributions to logic and "The American Enlightenment."

"2014 is the centenary of Charles Peirce's death, so I am particularly pleased to be invited to give this talk at the start of the year. I plan to place Peirce in the broader context of nineteenth century intellectualism and the development of Harvard University at the time."

Monday, April 23, 2012

Logic And Computation As Biophysics

The elusive mechanics of natural logic is by definition the mechanics of biophysics, describing how sense is characterized and how the biophysical structure is moved from apprehension to action. I will argue that this mechanics is fundamental to the inquiry of logic, determining the natural laws of logic, and that it is time for logicians to return to these foundational issues as theoretical biophysics, a field in which a wealth of new data promises to inform us.
I present the current state of my inquiry: a new logic and model of computation based upon the function of flexible closed manifolds describing how sense is characterized, symbolic processing, and covariant response potentials, the analogs of biophysical cells and multicellular membranes and their associated mechanics. The mathematization of this approach formally requires a unification of logic and geometry. I will present steps toward the specification of such a logic and its geometric implementation in dynamic structure designed to enable the explanation and reproduction of biophysical function. And I will speak to the predictions of the theory concerning the mechanisms that remain to be discovered.
"Logic And Computation As Biophysics" by Steven Ericsson-Zenith is the abstract for a presentation at the Stanford University Mathematical Logic seminar on May 8th, 2012.

Thursday, February 16, 2012

Conceptions Of Locality In Logic And Computation, A History

Is the logical assembly of the parts sufficient to determine the whole? Or is it, rather, the inverse, that the parts are determined as logical differentiations of the whole? And if so does anything remain of the whole that is not characterized by the logical relations between the parts? Are these two views equivalent, i.e., does the fact of the matter make any difference to logical results?
These questions relate to the mechanics of the structure that is the natural basis of logical operations. A way to view the question is to ask if this base mechanics is either differentiation in dynamic manifolds of sense, as suggested by our biology and experience, and in which the mechanisms of sensory characterization may play a role; or the construction of discrete logical parts and the relations between them. Before the current era, resplendent with computing machinery constructed upon the latter view, versions of the manifold argument were often preferred, notably in the algebraic logic of Peirce-Schröder.
The necessity to provide a computable explanation of sensory characterization and bound response potential in biophysics justify a review of the matter. A review is further justified by the search for a computable solution to general recognition, a ready operation in biology that is imperfect and costly, and may be intractable in its general form, in current computing architectures.
Central to the question is the nature of the inference mechanism determined by the basis structure of logical systems. Can we say, for example, that presented with A and B that the logical combination of the two loses nothing of their natural implication? Can we extend such a claim when presented with A and B and C etc..?
We may also question whether it is always reasonable to assume that the logical product of A and B combined is immutable in the presence of all other terms? In other words, are logical compositions side-effect free as the atomic view insists, or are there hidden factors that are not accessible to it?
In the atomic, analytic, view all derived logical values have equal standing to their premises and a logical expression describes the composition of atoms. The interpretation of combining these atoms in a logical expression is either independent of any a priori binding or it is considered to capture or impose such a binding.
The manifold view can be given clear geometric correspondents, “shapes” ( “symbols” or “signs” ) upon the manifold characterize the parts. The manifold provides a natural, continuous, and unifying dynamics binding them, inference in this view is a transformation of the manifold. We must consider therefore whether the atomic view is sufficient to characterize the behavior of such manifolds and to do so we must identify the difference that this makes to results.
Certainly, Charles Sanders Peirce (1839-1914) did not consider the atomic view sufficient, unlike Frege he was not concerned with mere statements of truth but rather the differences the apprehension of such statements identify in the world, and he was critical of directions being taken by his contemporaries (notably Bertrand Russell) that ignored these considerations. Of Russell's algebra, as of 1904, Peirce wrote to Victoria Welby:
 The criticism which I make on that algebra of dyadic relations ... is that the very triadic relations which it does not recognize it does itself employ. For every combination of relatives to make a new relative is a triadic relation irreducible to dyadic relations. 
Charles Sanders Peirce. Letter to Victoria Welby. (October, 1904)
Peirce is essentially arguing that the interpretant manifold of the logician (called “thirdness” in Peirce's vocabulary, hence “triadic” ) is a necessary addendum for the correct interpretation of such logical text, i.e., the effective results, to be viewed as behavioral outcomes according to Peirce's Pragmaticism, between a purely mechanical interpretation of the dyadic relations according to the principles of modern computable inference differ from the natural manifold interpretation because there are factors inaccessible to the interpretation of purely atomic (dyadic) relations.
Christine Ladd-Franklin (1847-1930), Peirce's doctoral student at John Hopkins University, continued this criticism against the “Russellisation” of logic long after Peirce passed. We will explore Peirce's view in some detail and briefly discuss the contributions of his students.
In this presentation we will consider the question and the diverse historical views related to it during the period from Charles Sanders Peirce (1839-1914) to Alan Turing (1912-1954), especially including a review of the contributions of Ernst Schröder (1841-1902) and Rudolf Carnap (1891-1970) compared to Gottlob Frege (1848-1925), Bertrand Russell (1872-1970), and Alfred North Whitehead (1861-1947), and the influence of Clarence Irving Lewis (1883-1964) and Cooper Harold Langford (1895-1964).

The above is the abstract of an invited presentation for the Special Session "The Universal Turing Machine, and History of the Computer" of CiE Centenary Celebration of Alan Turing to be held in Cambridge, England in June 2012 and fortcoming paper: "Conceptions Of Locality In Logic And Computation, A History" by Steven Ericsson-Zenith. It provides the historical context for logic as manifolds v. logic as atoms.

Tuesday, February 14, 2012

Computing With Structure

In this presentation we propose realizable mechanisms for computable logic founded upon a structural theory of logic, sensory characterization, and response potential in closed manifolds.
Briefly, the mechanics of differentiation, in which the mechanisms of sensory characterization play a role, upon the surface of a closed manifold characterize logical elements (signs) and naturally covary with the mechanical response potential of the structure. The manifold provides a natural, continuous, and unifying dynamics binding these elements. Inference is a transformation of the manifold.
We suggest that these mechanisms are observable in nature. In biophysics it is structure and the concurrency of action that are first-order considerations. It is the shape of single cells and multicellular membranes ( “closed manifolds” in mathematical terms) that characterize sense and modify action potentials that produce behavior.
A generalization of the existing evidence suggests that symbols form directly upon the surface of these manifolds in cell and membrane architectures, the processing of which constrains biophysical action potentials associated with the structure. This close binding of symbol processing and action potential is naturally formed by the evolutionary process.
Symbolic processing in the biophysical system is profoundly efficient. Storage is free and the capacity for symbol representation is combinatorial across dynamic sensory manifolds. This simple efficiency suggests general engineering principles that offer significantly greater symbolic processing capability in biophysical architectures than previously considered.
In contrast, parallel computation as we understand it today is decomposable, a second order consideration of the Turing model. Parallelism can be semantically removed from computer programs with no discernible effect upon the results. Therefore it contributes nothing algorithmically, providing only performance semantics.
The parallelism that we consider here makes a difference. As in biophysical systems, structural parallelism is not decomposable without impact upon the results. It plays a role algorithmically, providing the mechanisms of recognition and memory in the surface conformations of the processing architecture. Large scale differentiation appears in the dynamics of these closed manifolds and result in measurable characteristic behavior suggesting new architectures for recognition and prediction.
Two opposing views concerning the nature of Logic will concern us. The first, represented in the variety of models of computation considered by Alan Turing[1][2], is the view that logical operation is the integration of symbolic elements. The second is the view, suggested by Rudolf Carnap[3], that the basic relation is “recollection of similarity” (recognition) and computable Logic is “differentiation from the entirety of sense,” in which symbolic elements are continuously bound by the originating whole.
Our goal here will be to show that these two views, and the realizable mechanisms that they represent, are distinct and that their operation produces different results. In particular, the models of Alan Turing represent a metaphysical view in logic that has no capacity for the basic relation of Carnap and results in prohibitive storage and value distribution requirements.
To effectively construct such machines we require the development of a new computational logic, one that deals with differentiation, structural conformation, and related action potentials. We will outline our first steps toward such a logic.
This approach suggests a new pragmaticist foundation for logic (and potentially a new mathematics to be built upon it) since it eliminates the integration of traditional truth values in favor of symbolic differentiation upon closed manifolds and the transformation of the associated structure.

1. Turing, Alan. On Computable Numbers, With An Application To The Entscheidungsproblem. (1936).
2. Turing, Alan. Intelligent Machinery, A Heretical Theory. (1951).
3. Carnap, Rudolf. The Logical Structure Of The World. Open Court (1928). ISBN:0812695232.

This presentation is an invited talk for the conference The Incomputable, an Isaac Newton Institute for Mathematical Sciences event held at the Royal Society's Chicheley Hall in England in June 2012. The Incomputable is a major workshop of the 6-month Isaac Newton Institute programme - "Semantics and Syntax: A Legacy of Alan Turing."

Sunday, January 29, 2012

Toward The Unification Of Logic And Geometry As The Basis Of A New Computational Paradigm

In his "Aufbau" Rudolf Carnap (1891-1970) proposed that logical operations are differentiation from the entire manifold of sense and proposed "recollection of similarity" as the basic relation. This view fundamentally differs from the conventional mechanics of Alan Turing (1912-1954), that treats computable logic as the mechanical integration of logical atoms.
This view, that logic be founded upon manifolds and not discrete logical atoms, is not new and was not uncommon before Alan Turing's Universal Machine model of computation became pervasive, popularized during the critical period founding mathematical logic by the work of Ernst Schröder (1841-1902), influenced greatly by Charles Sanders Peirce (1839-1914). 
A common argument against the manifold view is that it makes no difference to computed results. Yet this argument is refuted when confronted by the challenges of general recognition and of locality in contemporary large scale parallel computation.
We present work toward the development of realizable mechanisms for computable logic based upon a re-conception of logic as operations of differentiation upon closed manifolds. This approach requires a unification of conceptions in logic with natural geometric transformations of closed manifolds, combining symbol processing with response potential. 
Confirmation of these mechanisms may exist in nature, in dynamic biophysical structure. Our investigation is founded upon the premise that it is the structure of closed manifolds in biophysical architectures thatcharacterize sense and closely bind sense to directed response potential.
The presented exploration is experimental and purely mathematical. The approach argues that the effects we seek to characterize have a natural mathematical basis and that by the elimination of naive assumptions concerning apprehension from geometry a characterization of Carnap's basic relation will suggest itself. We take this approach because it is the action of such apprehension that is the subject of our exploration.
The resulting mechanics suggests the design and physical realization of a new model of computation; one in which structure and the concurrency of action are a first-order consideration. By this model symbolic processing is storage free and closely bound to response potentials, the capacity of symbol representation is combinatorial across these dynamic manifolds, suggesting general engineering principles that offer significantly more symbolic processing capability in biophysical architectures than previously considered.
Carnap, Rudolf. The Logical Structure of the World. Open Court (1928). ISBN:0812695232. 
Schröder, Ernst. Vorlesungen über die Algebra der Logik. (1890) [Vol.I-III] (1910) 
The above is the abstract of a presentation submitted (and accepted) to CiE Centenary Celebration of Alan Turing to be held in Cambridge, England in June 2012 and fortcoming paper: "Toward the unification of logic and geometry as the basis of a new computational paradigm" by Steven Ericsson-Zenith. It provides the technical details of one of our approaches in current research.

Friday, January 6, 2012


Three theories
This work is concerned with the development and operation of sentient biophysical structure. The vehicle of our inquiry is an investigation into the foundations of logic and apprehension with respect to the mathematical characterization of such structure, its behavior, and its computable reproduction.
Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. By extension our inquiry brings together the traditional concerns of cosmology, computation, and epistemology.
Underlying this investigation is the broad range of contemporary biophysical observationand experimentation. Much of this observation and experimentation was impossible before the current era. The results are voluminous and often narrowly specialized. Theorists have, as yet, had little time to consider the broader implications.
These theories are based upon a new explanation of experience in nature, the construction of senses, and the operation of spontaneous biophysical behavior. This new approach is developed from first principles to enable a rigorous and systematic explanation of the variety of associated behaviors. 
The nature of our inquiry
Alongside this development is a further inquiry that focuses upon the nature of our work. It discusses the existential aspects of scientific inquiry, its epistemology and logic. It seeks to clarify the nature of the mathematical characterization and computation of natural behaviors, dealing with questions in the foundations of logic. It explores methodological issues related to reduction and the refinement of ideas from intuition to formal logical structure.
This second inquiry is the necessary complement to the first because it is an explanation that deals with its own foundation.
A calculus for biophysics
In support of this broad inquiry we work toward the development of a calculus for biophysical construction and its dynamics. The focus of this calculus is the structural dynamics for the range of single cells, multicellular architectures, and membranes. In our model it is the shape of these biophysical elements that characterize sense and modify action potentials producing motility, if successful this mechanics mathematically characterizes sensory and motile behavior.
Upon this foundation we propose a model of apprehension and explore how its products are processed by the organism. Finally, we propose  a probabilistic theory that enables us to reason about inaccessible factors in group behavior.
Three mathematical approaches
We follow three mathematical directions in anticipation that they inform each other. The first of these is the simple assertion that the basis of sense and spontaneous biophysical action is universally presentand by this simple presence structure assembles against it. This approach can only serve us if the mechanism characterizes a structural dynamic that is a consequence of this presence. The second direction is more conventional and follows a similar line of reasoning to the first except that it suggests the mechanism is the result of a covariant field effect upon the geometry of closed structures.
The third approach is radical and a purely mathematical exploration. It argues that the effects we seek to characterized have a natural mathematical basis and that if we eliminate naive assumptions concerning apprehension from a logical geometry then a characterization of the effect will suggest itself.
Rejection of emergence theory
You will note immediately that our approach is differential upon closed smooth manifolds and not founded upon a discrete particle theory. This is due to a recognition that neither construction from atoms nor the magic of emergence are viable existential explanations of our continuous and unfied experience, of sense.
A new computational mechanics
The mechanics we propose suggests the design and physical realization of a new model of computation; one in which structure and the concurrency of action are a first-order consideration. Symbolic processing in the biophysical system is storage free and the capacity of symbol representation is combinatorial across dynamic sensory manifolds, suggesting general engineering principles that offer significantly more symbolic processing capability in biophysical architectures than previously considered.
Proof in practice
We identify opportunities for experimental verification of the theory and we suggest a proof of our results in practice by the identification of this mechanism, allowing the construction of machines that experience.

Explaining Experience In Nature: The Foundations Of Logic And Apprehension is a series of technical volumes authored by Steven Ericsson-Zenith and published by IASE. Available by subscription only.