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in the 21st CENTURY


Two new modeling paradigms have appeared to support neural research in the 21st Century. The first is an expansion of the formalism associated with the Scientific Method. The second is a mechanistic transition from the archaic chemical theory of the neuron to a more comprehensive and better founded Electrolytic Theory of the Neuron.

last Update: 1 June 2012


Understanding the Neural System at the most basic level is required if its operation can be exploited effectively in the fields of medicine and bioengineering during the 21st Century. A major problem has arisen in the nonlinear and nonstationary character of some of the mechanisms, particularly those associated with the stage 1 sensory neurons of the various sensing modalities; vision, hearing, taste, smell and touch in the case of the external sensory modalities. These nonlinearities and non--stationary characteristics require familiarity with some very sophisticated mathematics and some of the latest additions to the technological toolbox of Man. Otherwise, the Deductive approach to system analysis fails significantly. this webpage is supported by a broader discussion to be found in Chapter 7 of the online book, "The Neuron and Neural Systems of Biology."

Marmarelis versus Popper: a broader Synergistic Approach

At the Theoretical level, the New Synergistic Approach to the Scientific Method of Marmarelis involves an Inductive portion and a Deductive portion. This two-step approach improves on the deductive approach of Popper that dominated the 20th Century and led to the slowing of basic scientific research during the later quarter of that period. During the Inductive phase, a more serious effort is made to "listen to the laboratory data" and evolve a null hypothesis that is more clearly defined than the largely conceptual hypotheses generated during the Deductive phase of Popper. The subsequent falsification process of Popper becomes more focused and less argumentive.

Researchers employing the Deductive approach to the Scientific Method, even following the dictums of Popper have been failing regularly in their attempts to move the knowledge base forward. This can frequently be attributed to their lack of a sufficiently broad mathematical understanding of, or approach to, the problem. To overcome the problems described above, Marmarelis has introduced a broader Synergistic approach to system analyis. His approach employs two distinct logical phases, the Inductive phase and the Deductive phase.

Marmarelis has recently introduced a new method of analysis applicable to any system but particularly driven by the need to analyze biological systems at the most fundamental level. He has provided a very broad mathematical framework that goes beyond the linear differential equation environment usually assoumed for biological systems. In theory, his approach is able to treat both nonlinear differential equations and non-stationary differential equations. While his limited number of examples using these more sophisticated environments have not been particularly successful, they do point the way to greater progress and understanding of the biological system.

The widely recognized adaptive properties of each of the external sensory modalities are clear demonstration of the nonlinear and non-stationary character of at least some of the circuits of the neural system.

The Synergistic approach, and particularly the Inductive phase, does require the broadening of the investigators perspective of possible mechanisms. It must include the potential for both an Electrolytic Theory of the Neuron as well as the older Chemical Theory of the Neuron. The results of the Inductive phase will speak for itself and point toward the Electrolytic Theory as providing the better and more concise solutions (see below).

The SYNERGISTIC approach to system modeling

The Synergistic approach involves two distinct phases, an Inductive phase where the mathematics of the input/output transfer function of the circuits of interest speak to the investigator. The transfer function defines the potential underlying processes, under the assumption that the mathematical framework employed is broad enough.

It is obviously necessary to employ nonlinear differential equations to represent a nonlinear mechanism. Similarly, it is necessary to emply non-stationary differential equations to represent a non-stationary mechamism. The initial adaptation amplifier of each sensory neuron of each external sensory modality clearly requires a differential equation framework able to accommodate both of these environments unless carefully devised protocols are devised to limit the operation of the mechanisms under study.

The cited 1989 paper by Marmarelis introduces the additional mathematical concepts needed to pursue the Inductive approach to the Scientific Method. The 2003 book, codifies the additional mathematical concepts required and gives multiple examples using the Synergistic Methodology to System Analysis.


The earlier DEDUCTIVE approach to modeling

Restating the philosophical underpinning of the Scientific Method espoused by Popper;

A Theory, to be scientifically valid, must be empirically testable (falsifiable) in the laboratory. Otherwise, it falls outside the realm of science. Such an untested theory is currently called a "null hypothesis." If the empirical investigation shows it is valid, it is accepted as useful and the hypothesis is recognized as a valid theory (at least for the time period).
If the empirical investigations of the period (or a later period) develop data in conflict with the null hypothesis, the hypothesis is refuted and must be discarded or restated (based on the new data).
In many pedagogical situations, a null hypothesis in conflict with the complete data set is allowed to stand as a "first order theory" while a new null hypothesis is proposed as a more advanced or second order theory. Unless the falsifiability of the old null hypothesis is stressed, this is a poor method of teaching. This situation is not always recognized or honored within the academic community.

The Electrolytic Theory of the Neuron replaces the archaic chemical theory

The Chemcial Theory of the Neuron emerged during the late 1800's during a period of;

As a result, the Chemical Theory of the Neuron grew with the empirical data base within the histological and physiological laboratories of the early 20th Century. A majority of the expansion of the Theory occurred in the first half of the 20th Century;

A new Electrolytic Theory of the Neuron, a.k.a., the New Neuron Doctrine has emerged during the preparation of this work that answers many questions left unanswered by the previous chemical theory applied to neuroscience. The Electrolytic Theory is also able to answer questions that have not even been formulated under the chemical theory. It will be summarized here to reflect the material developed above and to provide a preview of the material to follow.

The wording below is one of two. An alternate wording can be found in Section 2.6.2 of the Introductory Chapter of "The Neuron and the Neural System: An Electrolytic Paradigm" downloadable from the document page of this website.

The Electrolytic Theory begins with a basic axiom

The Neural system of biology is based on;

Corollaries to this axiom include,

The Neuron interpreted using the Electrolytic Theory

The basic neuron can be described in considerable detail based on the Electrolytic Theory. Go to Fundamental Neuron Architecture to review this material.

The Neural System Architecture based on the Electrolytic Theory

The neural system can be described in considerable detail based on the Electolytic Theory. Go to Neural System Architecture to review this material.

Return to the Neuron Research home page.


Marmarelis, V. (1989) Volterra–Wiener analysis of a class of nonlinear feedback systems and application to sensory biosystems In Advanced Methods of Physiological System Modeling, Vol. 2 NY: Plenum

Marmarelis, V. (2003) Prologue and Introduction In Nonlinear Dynamic Modeling of Physiological Systems. NY: Wiley–Interscience

Fulton, J. (2010) The Neuron and Neural System: An Electrolytic Paradigm. http://neuronresearch.net/neuron/document.htm

McGeer, P. Eccles, J. & McGeer, E. (1987) Molecular Neurobiology of the Mammalian Brain. NY: Plenum Press.