Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large number of (...) comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations. (shrink)

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

In Things That Make Us Smart, Donald A. Norman explores the complex interaction between human thought and the technology it creates, arguing for the development of machines that fit our minds, rather than minds that must conform to the machine.Humans have always worked with objects to extend our cognitive powers, from counting on our fingers to designing massive supercomputers. But advanced technology does more than merely assist with thought and memory—the machines we create begin to shape how we think and, (...) at times, even what we value. Norman, in exploring this complex relationship between humans and machines, gives us the first steps towards demanding a person-centered redesign of the machines that surround our lives. (shrink)

There are several key ingredients common to the various forms of model-based reasoning considered in this book. The term ‘model’ comprises both internal and external representations. The models are intended as interpretations of target physical systems, processes, phenomena, or situations and are retrieved or constructed on the basis of potentially satisfying salient constraints of the target domain. The book’s contributors are researchers active in the area of creative reasoning in science and technology.

In this path-breaking work, Paul Thagard draws on history and philosophy of science, cognitive psychology, and the field of artificial intelligence to develop a ...

The book Model-Based Reasoning in Scientific Discovery, aims to explain how specific modeling practices employed by scientists are productive methods of ...