The mind has been called one of the final frontiers of science, and rightly so: basic concepts familiar to us all have yet to be modelled and understood, such as the vivid feeling of emotions or the vague notion of consciousness that seems vital to the core of our being. The primary approach in cognitive science, the study of mind, is that of taking a functionalist view: this view attempts to replicate the higher-level functioning of the brain without unduly concerning itself with the lower-level processing and underlying dynamics that must be inherent in such a complicated structure. Yet a smaller camp is beginning to make headway: this camp concerns itself with a dynamic systems approach and it attempts to reconstruct the brain from the ground up using neuroscience data as a basis.Go BackNeuroscience studies based on actual readouts and graphical representations of the brain are beginning to make more of an impact; because these studies are delving into areas previously uncharted, they are providing a vast amount of insight into the study of the functioning of the mind and its interaction with the body. It is necessary to combine this information with the broader understanding of the brain's processes so that a more complete and robust model can be created from the interaction of the lower-order basic principles with the higher level functioning. Like a computer is dependent on its electric components to provide a stable foundation for its applications, so should the study of the mind be looked at from a bottom-up approach so as to provide structure to the varying higher-level models presented.
A bit of explanation is clearly necessary; though the realm of cognitive science is interdisciplinary in nature, it is still emerging as a field and is often overlooked. This short background page will explain some of the basic functioning of the mind and the interaction of brain cells, so that a better understanding of the dynamics and possible fractal-like structure can be appreciated.
The fundamental unit of the brain is termed a neuron -- this is just the scientific term for a single brain cell. Without going into too much detail, a neuron communicates to other neurons via electrical impulses, also called potentials, and chemical secretions whose effect is not well understood. Electrical input to one neuron comes from many others, each having a specific amount of influence, or weight, on the neuron. This input is collected by the neuron and then an implicit mathematical function is used to determine the amount of output the neuron produces. This function is often a threshold function, so that the neuron will solely output after the sum of its inputs is greater than a certain limit. In other cases, the neuron uses a linear function directly corresponding to the sum of its inputs received to output an electrical signal. Though solely using linear functions, with enough neurons any other function, linear or non-linear, can be approximated.
Groups of neurons are often connected in multi-layered local or distributed networks, where each sole neuron is explicitly or implicitly working with other neurons to perform a specific task. These networks have been modelled with some success by neural network structures and connectionist systems; they are used in artificial intelligence applications such as speech recognition and image reconstruction.
Anyway, when neuronal networks are activated, they produce a noticeable change in voltage potential which can be captured by an electroencephalogram (EEG). The brain is connected to an electrode which outputs an EEG reading recording a plot of this voltage against time. A couple of sample EEG graphs from a cat before and after a cocaine dose are shown in the PMATH399c text, "Encounters with Chaos" on p. 27. Yet much more revealing and startling information can be determined from EEG scans by looking at the box-counting dimension of the EEG and the possible presence of strange attractors, at which point the energy of the neural net is sensitive to initial conditions. The importance of chaos in the brain will also be discussed. This will be the topic at the core of this part of my research project and the subject of my next section.