  At what level should government or companies support research? This complex
multi-faceted question encompasses such qualitative bonus as satisfying natural
human curiosity, the quest for knowledge and the impact on education and
culture, but one of its most scrutinized component reduces to the assessment of
economic performance and wealth creation derived from research. In certain
areas such as biotechnology, semi-conductor physics, optical communications,
the impact of basic research is direct while, in other disciplines, the path
from discovery to applications is full of surprises. As a consequence, there
are persistent uncertainties in the quantification of the exact economic
returns of public expenditure on basic research. Here, we suggest that these
uncertainties have a fundamental origin to be found in the interplay between
the intrinsic ``fat tail'' power law nature of the distribution of economic
returns, characterized by a mathematically diverging variance, and the
stochastic character of discovery rates. In the regime where the cumulative
economic wealth derived from research is expected to exhibit a long-term
positive trend, we show that strong fluctuations blur out significantly the
short-time scales: a few major unpredictable innovations may provide a finite
fraction of the total creation of wealth. In such a scenario, any attempt to
assess the economic impact of research over a finite time horizon encompassing
only a small number of major discoveries is bound to be highly unreliable. New
tools, developed in the theory of self-similar and complex systems to tackle
similar extreme fluctuations in Nature can be adapted to measure the economic
benefits of research, which is intimately associated to this large variability.
