As Physics did in previous centuries, there is currently a common dream of
extracting generic laws of nature in economics, sociology, neuroscience, by
focalising the description of phenomena to a minimal set of variables and
parameters, linked together by causal equations of evolution whose structure
may reveal hidden principles. This requires a huge reduction of dimensionality
(number of degrees of freedom) and a change in the level of description. Beyond
the mere necessity of developing accurate techniques affording this reduction,
there is the question of the correspondence between the initial system and the
reduced one. In this paper, we offer a perspective towards a common framework
for discussing and understanding multi-level systems exhibiting structures at
various spatial and temporal levels. We propose a common foundation and
illustrate it with examples from different fields. We also point out the
difficulties in constructing such a general setting and its limitations
