This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modeling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.

The integration of mathematics with physics, molecular and cell biology, and the neurosciences, will constitute the new frontier and challenge for 21st century science, where breakthroughs are more likely to span across traditional disciplines.

Mirroring Brains combines neuroscience, psychology and philosophy to provide a comprehensive account of one of the most intriguing discoveries of the last 30 years-the discovery of mirror neurons. These neurons are characterized by firing both when someone performs an action, and also when they observe the same action being performed by others. Whereas it was widely regarded as characteristic of only a small subset of neurons, recent discoveries have shown that the mirror property is a fundamental principle of the functioning of the whole brain. Exploring this discovery, Rizzolatti and Sinigaglia explain how we are able to immediately understand others' actions and emotions, providing a deeper understanding of how we relate to each other and introducing the idea of 'understanding from the inside'. Mirroring Brains provides a new interpretation of the property and function of mirror neurons, allowing readers an insight into a fundamental principle of brain function. Rizzolatti and Sinigaglia provide a rich survey of the main neuronal and psychological findings concerning the mirror mechanism, plus an extensive discussion of its potential role in social cognition. It is an essential read for neuroscientists, psychologists, philosophers, sociologists, and anyone who is interested in understanding how we relate to each other.