ABSTRACT
In order for mathematics to be used in the modeling of physical events there must exist a definable mapping between number, which is a mental construction, and dimension, which is a property of a physical object. In most instances this is trivial. However, in competitive dynamical systems, such as most neural networks that are used to model biological systems, it is possible for the system to require a different mathematical representation of number at each time step if there is no a priori way for the system itself to have an absolute and invariant representation of ‘number’. This situation occurs when a change in the value of a mathematical variable implies, not only a change in the value of some physical dimension but also a change in the systems ability to measure information and hence its representation of number. Computer simulations of biological competitive systems are also subject to this criticism because a computer has an absolute and invariant representation of number, as does the mathematics it simulates; but the biological system to which the analogy is then made does not necessarily have this same invariance. In biological systems it is very likely that the state of the system affects its ability to interpret information.
