In recent years, most of the behavioral sciences have seen a heavy influx of influence from the neurosciences. Most obviously, the psychology of only three decades ago was almost bereft of brain-related talk. Now, however, one of the fastest growing areas of psychology is cognitive neuroscience, whose practitioners regularly talk of neuroanatomy and neurophysiology, and employ various brain imaging and measurement techniques, like fMRI and EEG. The same trend can be found in many other disciplines as well, including linguistics, economics, and philosophy.

While the growing influence of neuroscience is undeniable, it would be a mistake to think that the field of neuroscience itself is monolithic. Quite the contrary: the tens of thousands of posters and presentations at the Society for Neuroscience meeting held every year are divided into many sections, such as molecular neuroscience, cellular neuroscience, systems neuroscience, neuroanatomy, developmental neuroscience, behavioral neuroscience, cognitive neuroscience, and so on. Often, the researchers in one area are not able to understand or communicate effectively with those from another, despite the fact that ultimately, everyone in the building wants to understand how the brain works.

This, of course, is not a problem unique to neuroscience. Many other areas of biology suffer the same difficulties, as do other sciences such as geology, chemistry, and even physics. However, one main advantage that, for example, physics has in mitigating these challenges is a widely shared technical vocabulary for describing both problems and solutions in the field. The development and application of these quantitative tools have helped physics develop rapidly, leading us to exciting new discoveries, as well as deep, challenging problems. The subfield of physics most centrally concerned with the development of such tools is theoretical physics.

Interestingly, an analogous subfield has been developing in neuroscience over the last few decades as well, and it is often appropriately called “theoretical neuroscience” (though perhaps equally as often called “computational neuroscience”). In fact, the analogy between theoretical neuroscience and theoretical physics is quite useful for understanding the importance of theoretical neuroscience to neuroscience in general. For instance, both theoretical physics and theoretical neuroscience are centrally interested in quantifying the phenomena under study. This does not mean merely statistically quantifying the data generated by the phenomena, but rather coming up with quantitative descriptions of the deterministic regularities and mechanisms giving rise to those data. Take, for instance, one of the greatest advances in theoretical physics, the development of Newton's three laws of motion. The second, perhaps most famous, law is that “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed” (Newton, 1729, p. 19). In short form: F=ma. The purpose of this statement is to make a clear, straightforward hypothesis about motion. I describe similar principles in the sections about neural representation, transformation, and dynamics.

A second analogy between these two subfields is that both are interested in summarizing an enormous amount of data. Newton's second law is intended to apply to all forms of motion, be it rectilinear, circular, or what have you. Measuring all such forms of motion, and describing the results statistically would not be nearly as concise. Similarly, theoretical neuroscientists are attempting to understand the basic principles behind neural function. Often, they would like their mathematical descriptions to be as general as possible -- although there is some debate regarding whether or not the kind of unification being striven for in physics should be a goal for theoretical neuroscience.

A third crucial analogy between theoretical physics and theoretical neuroscience is that the disciplines are speculative. Most such quantitative descriptions of general mechanisms go beyond the available data. As such, they almost always suggest more structure than the data warrants, and hence more experiments to perform. Looking again to Newton's second law, it is clear that Newton intended it to be true for all velocities. However, special relativity has subsequently demonstrated that the law is measurably violated for large velocities. With speculation comes risk. Especially for a young field like theoretical neuroscience, the risk of being wrong is high. But, the risk of becoming lost in the complexity of the data without such speculation is much higher. The real fruit of a field like theoretical neuroscience -- fruit realized by theoretical physics -- is (hopefully) the identification of a set of principles that lets massive amounts of data be summarized, thereby suggesting new questions and opening lines of communication between different sub-disciplines.

Of course, there are crucial disanalogies between these fields as well. For instance, we can think of physics as being interested in questions of what there is, while neuroscience is interested in questions of who we are. As well, neuroscience is a much younger discipline than physics, and so the methods for making measurements of the system of interest are still rapidly developing.

Nevertheless, the similarities can help us understand why theoretical neuroscience is important for the development of neuroscience. Like theoretical physics, theoretical neuroscience can help in at least two crucial ways. Specifically, it should:

1. Quantify, and hence make more precise and testable, hypotheses about the functioning of neural systems;

2. Summarize large amounts of experimental data, and hence serve to unify the many sources of data from different “neuro-” and behavioral sub-disciplines.

The first of these stem from the commitment to using mathematics to describe principles of neural function. The second is crucial for trying to deal with the unavoidable complexities of neural systems. This is a challenge not faced to the same degree by many physicists. Characterizing a system of billions of parts as if each is identical, and as if the connections between all of them are approximately the same can lead to very accurate characterizations of physical systems (e.g. the ideal gas law). The same is not true of neural systems. Large neural systems where all of the parts are the same, and interact in the same way simply do not exist.

Thus, the links between the “lowest” and “highest” levels of characterizing neural systems are complex and unavoidable. It is perhaps in this kind of circumstance that quantification of the system of interest plays its most crucial role. If we can state our hypotheses about neural function at a “high” level, and quantify the relationship between levels, then our high-level hypothesis will connect to low-level details. In fact, ideally, a hypothesis at any level should contact data at all other levels. It is precisely this kind of unification of experimental data that is desperately needed in the behavioral sciences to support cross-disciplinary communication, and eventually a mature theory of biological cognition.

This ideal role for theoretical neuroscience has not yet been realized. Perhaps this is because there has historically been more of a focus on “low” levels of neural systems (i.e. single cells or small networks). This is perfectly understandable in light of the complexity of the system being tackled. Nevertheless, I believe we are now in a position to begin to move past this state of affairs.

In the context of this book, I will adopt methods from theoretical neuroscience that I believe currently have the best potential to realize this ideal role. At the same time I hope the contents of this book will prod theoretical neuroscientists to consider expanding the viable areas of application of their methods to all of the behavioral sciences. In the next section I introduce a series of theoretical principles developed in the context of traditional theoretical neuroscience. In subsequent chapters I suggest a way of applying these same principles to large-scale, cognitive modeling. This should help to not only test, but also to refine such principles, and it will help make our cognitive models subject to data from all of the various disciplines of the behavioral sciences.