Science has slowly evolved over many centuries from its origins as a branch of natural philosophy. It is now a growing, formalized and rather powerful collection of systematized knowledge and methodologies for gathering knowledge. In part its success has been due to the continuous refinement of a simple but relatively rigid code of detached observation, logical formalism, repeatability, reductionism and rigour. This approach to studying our environment has literally made it possible to reach the moon.
However, a price has been paid. Science has gained power by denying or excluding the nature of anything which cannot be formally described in scientific terms. True to form, this is not an outright denial or suppression of evidence. Science is after all bound by its own principles to accept and adapt to that which is incontrovertible or at least verifiable. Rather it is a subtler form of denial involving the reduction of ideas, things and experiences into simple pieces which are consistent with science in the Gödelian sense. Complex systems often suggest inconsistencies which cannot be resolved and subsequently they must be reduced to something less than they are.
Visualization works out of the grey area of human perception and cognition. So far it has not been found to be self-consistent; there are no rules which precisely govern what approach will work under a given set of conditions. Visualization is not strictly repeatable; one user may perceive a relationship (which may not be verifiable using visualization techniques) while another sees nothing at all or something entirely different. Visualization relies on subjective interpretation; contextual cues are usually derived from ``common" experience which are neither guaranteed to be common or commonly integrated into personal experience. Visualization is resistant to the systematic evaluation and assessment procedures common to science; it still remains difficult to ascertain if a particular instantiation has been ``successful".
So how does it contribute to science at all? Visualization is part of a process of discovery. It appears to aid the intuition in identifying relationships, some of which can be later described by formal analysis. In cases where there is no such analysis, the results of visualization cannot be properly integrated back into the scientific domain. Images like those of the Mandelbrot set are uniquely compelling, far beyond the trivial analytic evaluations of it which have been produced to date. Consequently the process of visualizing has been limited by the requirements of the science which seeks to exploit it. And at the same time, it offers inconsistencies that create problems for the scientist. It is from this quandary that we seek to free ourselves. And there may actually be solutions which are satisfying for both science and visualization.