wildcat2030: A complex system can, in principle, be observable – that is, the system’s complete internal state can be reconstructed from its outputs, which would ostensibly involve describing in complete quantitative detail all of its internal state variables at once. In an actual experiment, however, such measurement is typically beyond our reach, and so is limited to a smaller number of those variables. Referred to as sensors (or sensor nodes), these key variables can be used to make the complete system observable. Recently, scientists at Northeastern University and MIT devised a graphical approach that first derives the math­e­mat­ical equa­tions describing a complex system’s dynamics, and then determines the key sensors for that system. Moreover, when applying their approach to biochemical reaction systems, the researchers discovered that the derived sensors were both necessary and sufficient to describe the complete system. The scientists conclude that their findings allow a systematic exploration of many diverse natural, technological and socioeconomic systems. (via Through a sensor, clearly: Complex systems made observable)
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wildcat2030:

A complex system can, in principle, be observable – that is, the system’s complete internal state can be reconstructed from its outputs, which would ostensibly involve describing in complete quantitative detail all of its internal state variables at once. In an actual experiment, however, such measurement is typically beyond our reach, and so is limited to a smaller number of those variables. Referred to as sensors (or sensor nodes), these key variables can be used to make the complete system observable. Recently, scientists at Northeastern University and MIT devised a graphical approach that first derives the math­e­mat­ical equa­tions describing a complex system’s dynamics, and then determines the key sensors for that system. Moreover, when applying their approach to biochemical reaction systems, the researchers discovered that the derived sensors were both necessary and sufficient to describe the complete system. The scientists conclude that their findings allow a systematic exploration of many diverse natural, technological and socioeconomic systems. (via Through a sensor, clearly: Complex systems made observable)

cab1729: Einstein’s Zurich Notebook Einstein’s search for general relativity spanned eight years, 1907-1915. Some periods were quiet and some were more intense. The moments when the great transition occurred, came sometime between the late summer of 1912, when Einstein moved from Prague to Zurich, and early 1913. If we could choose one time at which to look over Einstein’s shoulder and watch him work on general relativity, it would be this time.And that is just what we can do. For, found among his papers when Einstein died in 1955 was a small, brown notebook containing his private calculations from just this time. This is the Zurich notebook.
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cab1729:

Einstein’s Zurich Notebook

Einstein’s search for general relativity spanned eight years, 1907-1915. Some periods were quiet and some were more intense. The moments when the great transition occurred, came sometime between the late summer of 1912, when Einstein moved from Prague to Zurich, and early 1913. If we could choose one time at which to look over Einstein’s shoulder and watch him work on general relativity, it would be this time.

And that is just what we can do. For, found among his papers when Einstein died in 1955 was a small, brown notebook containing his private calculations from just this time. This is the Zurich notebook.

(via proofmathisbeautiful)

Source: pitt.edu