This article is helpful to all the intrepid workers and should be printed read fitted and studied as it contains seed value with extensible utility.
full article at link;
This link to full article it says volumes about our subject; physorg.com
How to Measure What We Don't Know
September 10th, 2009 By Lisa Zyga (PhysOrg.com) -- How do we discover new things? For scientists, observation and measurement are the main ways to extract information from Nature. Based on observations, scientists build models that, in turn, are used to make predictions about the future or the past. To the extent that the predictions are successful, scientists conclude that their models capture Nature’s organization. However, Nature does not reveal secrets easily - there is no way for observers to learn everything about a process, so some information always remains hidden from view; other kinds of information are present, but difficult to extract. In a recent study, researchers have investigated how to measure the degree of hidden information in a process (its “crypticity”) and, along the way, solved several puzzles involved in extracting, storing, and communicating information.
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In their study, James Crutchfield, Physics Professor at the University of California at Davis, and graduate students Christopher Ellison and John Mahoney, have developed the analogy of scientists as cryptologists who are trying to glean hidden information from Nature. As they explain, “Nature speaks for herself only through the data she willingly gives up.” To build good models, scientists must use the correct “codebook” in order to decrypt the information hidden in observations and so decode the structure embedded in Nature’s processes.
In their recent work, the researchers adopt a thorough-going informational view: All of Nature is a communication channel that transmits the past to the future by storing information in the present. The information that the past and future share can be quantified using the “excess entropy” - the mutual information between the past and the future.
Since the present mediates between the past and future, it is natural to think that the excess entropy must somehow be stored in the present, the researchers explain. And while this is true, the researchers showed that, somewhat surprisingly, the present typically contains much more information than just the excess entropy. The information stored in the present is known as the “statistical complexity.” The more information Nature must store to turn her noble gears, the more structured her behavior.
The information that manages to go unaccounted for - the difference between the stored information (statistical complexity) and the observed information (excess entropy) - is the “crypticity”. It captures a new and under-appreciated complexity of a process, something that goes above and beyond what is directly measured in observations. At a more general level, the researchers provide an explicit way to understand the difference between simply making predictions from data versus modeling the process’s underlying structure. |
