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In some fields, including parts of biology and physics, data come from controlled experiment, allowing close matching between theory and experimental results.  Experimental design is, of course, subject to a multitude of biases that may limit knowledge.  At least as important, in many fields and subfields, including cosmology, oceanography,macroevolution, and many social sciences, controlled experiments are impossible.  What facts are obtainable represent samples of what we would like to know in ways whose biases themselves may be hard to know.  For example, knowledge of classical history depends substantially on one man, Herodotus, and we do not know how additional accounts would change understanding of Greece, Persia, Babylon, and Egypt.  Strongly socially constructed observations, accidental experiments, and often a spare historical record form much of the known.  Systems may also be simply too large or long-lived to observe. At a theoretical level, what we see or live with may reflect bifurcations and the influence of frozen historical accidents, and represent one realization of stochastic processes that admit many possibilities. An example is the question of whether the genetic code is the only code possible in some broad sense.

From seminal papers of Goedel and Turing, the 20th century witnessed a stream of "impossibility" results, including undecidability, non-computability, and intractability.  Although these results may limit knowledge, their significance or implications for what is unknowable in a range of fields remains unclear.  Several results concern formal (mathematical) systems.  Although science uses mathematics, it also differs from mathematics.  Can we up the ante from Goedel's analysis of formal systems and prove impossibility results in specific areas of physical science?  What about in fields of life sciences such as cellular and molecular biology, where reliance on modeling and formal systems remains much less?  What about financial or political systems?