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To provide ideas for possible connections, in the table below red entries relate to common statistical benchmarks, while blue entries relate to possible Bayesian criteria for burdens of proof in matters of legal evidence. The bold entry on coin tossing simply illustrates the more general rule that N bits of surprisal is associated with tossing all heads, on the first toss of N coins.
Stay tuned as we begin to add examples from the world of correlation-first informatics...
This page is about empirical observation exercises which put students into the shoes of scientific investigators.
For the measurement of very small time differences and/or observations at extreme speeds, a variety of simulators capable of generating empirical data may come in handy. Simulators also have the advantage that we can change parameters like the speed of light at will, something that is much more difficult to do in everyday life.
The next-to-last two entries in the table simply apply Boltzmann's constant kB ≈ 1.38×10-23[J/natK] ≈ 0.957×10-23[J/bitK], which specifies the minimum ordered-energy that must be thermalized for each nat or bit of subsystem correlation-information [1,2], per Kelvin of ambient reservoir for dumping the heat. The hotter the ambient, the greater the availability cost of good information, which is one reason that cooled CCDs can provide images with more bits per pixel, and that global cooling may be preferable to global warming [3].
Related references:
Seth Lloyd (1989) "Use of mutual information to decrease entropy: Implications for the second law of thermodynamics", Physical Review A 39, 5378-5386 (link).
P. Fraundorf (2003) "Heat capacity in bits", Amer. J. Phys. 71:11, 1142-1151 (link).
E. T. Jaynes (2003) "Note on thermal heating efficiency", Am. J. Phys. 71, 180-183 (link).
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