  Is reduction always a good scientific strategy? Does it always lead to a gain
in information? The very existence of the special sciences above and beyond
physics seems to hint no. Previous research has shown that dimension reduction
(macroscales) can increase the dependency between elements of a system (a
phenomenon called "causal emergence"). However, this has been shown only for
specific measures like effective information or integrated information. Here,
we provide an umbrella mathematical framework for emergence based on
information conversion. Specifically, we show evidence that a macroscale can
have more of a certain type of information than its underlying microscale. This
is because macroscales can convert information from one type to another. In
such cases, reduction to a microscale means the loss of this type of
information. We demonstrate this using the well-understood mutual information
measure applied to Boolean networks. By using the partial information
decomposition, the mutual information can be decomposed into redundant, unique,
and synergistic information atoms. Then by introducing a novel measure of the
synergy bias of a given decomposition, we are able to show that the synergy
component of a Boolean network's mutual information can increase at
macroscales. This can occur even when there is no difference in the total
mutual information between a macroscale and its underlying microscale, proving
information conversion. We relate this broad framework to previous work,
compare it to other theories, and argue it complexifies any notion of universal
reduction in the sciences, since such reduction would likely lead to a loss of
synergistic information in scientific models.
