David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Acta Biotheoretica 31 (3):185-202 (1982)
A new theory for basic function in the nervous system has recently been proposed (Dempsher, J., 1979a, 1979b; 1980, 1981). The major basic themes of the new theory are as follows: (1) There are two fundamental units of structure and function, the fibre or conducting mechanism, and the neurocentre, where nervous system function as we know it takes place. (2) The nerve impulse is regarded as a mathematical event. The mathematics is the result of a prescribed fusion of energy and matter. (3) Nervous system function everywhere in the nervous system is mathematical. In the fibre, the prescribed fusion of energy and matter results in a number. In the neurocentre, the prescribed fusion of energy and matter results in a mathematical function. Basic function in the nervous system everywhere requires a transformation of a nerve impulse in the fibre into a nerve impulse in the neurocentre with opposing properties: The nerve impulse in the fibre is confined to the fibre; cannot sum with another nerve impulse; can travel long distances with constant form and velocity; curvature in space and time are not significant features; and it is regarded as a number. On the other hand, the nerve impulse in the neurocentre is confined to the neurocentre; can sum with other nerve impulses; cannot travel long distances - even in a very short distance, it changes form; curvature in space and time is a very significant feature; and it is regarded as a mathematical function.The approach to determine how one form of the nerve impulse is transformed into the other at the input region is based on two of the differences listed above: (1) The nerve impulse in the fibre cannot sum with another nerve impulse in the fibre, whereas in the neurocentre, several nerve impulses sum to form a larger nerve impulse. (2) The nerve impulse in the fibre is regarded as a number, in the neurocentre, it is regarded as a mathematical function. The commonality of (1) and (2) is that the properties defining the nerve impulse in the fibre are associated with the property ofdiscreteness, whereas, the properties defining the nerve impulse in the neurocentre are associated with the property ofcontinuousness. Thus, the basic theme of unification of function at the input region of the neurocentre is the transformation of a phenomenon with the property of discreteness into a phenomenon with the property of continuousness. The solution to this transformation is approached from two directions:biologic andmathematical. In the biologic approach, the unit element of the nerve impulse in the fibre terminations (as.u. as a wave of energy, a spike in the classical theory) fuses with a. calcium-binding protein causing the release of Ca++. The calcium ions then combine with another protein. Associated with the second reaction is a conformational change in the Ca++-protein complex and the unit element in the neurocentre, bs.u., is emitted. Individual bs.u. then fuse with acetylcholine; summation occurs andwave b is emitted. In the mathematical approach, the nerve impulse as a number, is partitioned into two numbers with a precise rule relating these two numbers. One possibility suggested is that the number can be regarded as the value of a trigonometric function. This value then gives rise to an angle with sides related in a ratio or proportionality fashion — a relationship with the property of continuousness, as contrasted with that of a single number, discreteness. Both biologic and mathematical approaches are united so as to suggest that the mathematical (trigonometric) function arose as the result of a fusion of energy (as.u. as a wave of energy) and the calcium-binding protein as matter; following this reaction, bs.u., with opposing properties, is emitted.
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