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The role of mathematics and theory in understanding the brain

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Understanding the brain as a system will necessitate the use of mathematics, physics, and engineering. Neuroscience is in need of appropriate theory that is experimentally tractable, in the sense that it can be informed by data, can reproduce data, and can make non-trivial testable predictions. Understanding ...

Understanding the brain as a system will necessitate the use of mathematics, physics, and engineering. Neuroscience is in need of appropriate theory that is experimentally tractable, in the sense that it can be informed by data, can reproduce data, and can make non-trivial testable predictions. Understanding emergent complex dynamics and phenomena requires mathematics to provide a universal language that can organize ideas and provide a structure that supports drawing logical causal inferences between interacting components. Why is mathematics critical to the study of neuroscience? As with any complex system, our qualitative reasoning abilities are limited, in the sense that we can only combine or extend a logically connected train of thought a finite number of steps ‘into the future’. Mathematics provides a formal structure of logical rules that we can use to follow a line of thought in a logically consistent manner towards some conclusion in a way that assimilates conceptual principles and details (e.g. data) even if we cannot immediately keep track of all the logical relationships between the details. For a complex system such as the brain we are not going to understand it as a system by considering the details of one protein or ion channel at a time. Experiments in isolation, such as studying individual mechanisms or observational phenomena, provide important ‘pieces’ towards understanding the brain, but an appropriate theoretical framework must be used to provide context. It can be argued that there are insufficient appropriate theoretical frameworks to understand the brain and its emergent properties. However, theory in an empirical science should be informed by data provided by experiments, both for the purposes of validation and in order to provide real world predictions for the development of further theory. Over abstraction and simplification of cellular and physiological processes can lead to theoretical results of limited relevance or impact because they cannot be related back to how the real brain works. Lastly, brute force analyses and numerical simulations of large data sets on their own do not necessarily guarantee mechanistic or deep insights into function. While there is a continuing explosion of data in neuroscience and a lot of descriptive quantitative analysis and modeling, there are limited theoretical frameworks and structures that provide deep insights into how the brain works. By analogy, neuroscience is today where physics was over 100 years ago. Contributing authors are asked to comment and provide their views on questions such as what role does mathematics have to play in neuroscience, how do we identify and bring in areas of mathematics that normally have not contributed to neuroscience, can neuroscience contribute to new mathematical ideas, what should be the balance between theory and computational simulations, and how do we best train students to achieve this? Author interested in contirbuting will provide different and contrasting perspectives on these questions, and will include neuroscientists, mathematicians, physicists, and neural engineers.


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