Maps are powerful, but imperfect, visualizations of the world. They are never true in any absolute sense; rather, they express certain aspects of the truth in ways that are useful for the task at hand, using rules and conventions that have to be understood in context. No flat map of Earth's curved surface can preserve both area and angle; some aspect of the reality is always distorted. So geographers have invented a plethora of projections that allow them to choose the distortions judiciously. One projection might sacrifice the accuracy of shapes and areas to preserve bearings, for example, whereas another might facilitate precision measurements in a field survey. But even this panoply often falls short — and can be downright misleading — when it comes to representing more abstract forms of information.

A classic example is the use of maps to visualize scientific and social data about nations, states or counties. Mapmakers usually do this by simply adding, say, a colour scale to represent the value of indicators such as disease outbreaks. In addition, because this technique by itself is often misleading — it takes no account of differences in population density, for example — the data are frequently normalized to per capita values. But this means that the map loses crucial data — in this case, total incidences.

The cartogram technique, in which the sizes and shapes of geographical areas are distorted to represent the population or some other variable, can overcome these issues and preserve the full richness of the data (see page 270). Used correctly, it can free statistics from the shackles of geography, allowing richer visualizations of anything from election results, to census tabulations, to species biodiversity.

Cartograms have yet to be widely adopted, despite being the best choice for many sorts of data. One reason is that initially they can seem confusing, as most viewers' brains are more at home with the size and shape of countries and states as they appear in an atlas. Another is that efficient algorithms to create not only cartograms, but many other forms of visualizations, have generally been the preserve of a handful of specialized laboratories. That is now changing.

IBM's Visual Communication Lab in Cambridge, Massachusetts, for example, has created Many Eyes (http://www.many-eyes.com). This free site provides the public with tools to create visualizations such as network diagrams, which depict nodes and connections within networks, and treemaps, which display hierarchical data as groups of nested rectangles. Similarly, Google Earth and other virtual globes are providing scientists and non-scientists with unprecedented tools for geographical visualization of data. The obvious, and perhaps unexpected, enthusiasm of the public for such visualizations suggests that it is a rich vein for educators and scientists, both to explain their own work and as a means to engage young minds in critical analysis of data.

Visualizations are not a panacea. The adage 'rubbish in, rubbish out' still applies. But when used well — and, in the future, when combined with emerging surface-computing and other interactive displays — visualization can provide different views of data that force us to ask new questions, and generate fresh hypotheses.

The flood of data now coming online and the emergence of new forms — such as the data on social networks, e-mail and mobile-phone patterns that are rejuvenating the social sciences — means that visualization will be increasingly important for scientists. Such diverse windows on data should also strengthen civil society by giving scientists and citizens alike the power to sift through the data generated by governments and other institutions, and to challenge their and our own preconceptions of the world.