Theorem:
Moving toward the negative of anything embedded in a higher-dimensional space reduces the orthogonality (and hence dimensionality) of your path with respect to the postive of that same thing.
Corollary:
X and anti-X are in cahoots, even when they don't act like it.
Ideas are only a pale shadow of the world around, but it's fun nonetheless to look for ideas that reflect reality as simply as possible. What can do this better than a reflective sphere?
various energies
We encounter energy in many applications with different units. The quantities in the first units menu of this widget provide clues to how they relate. Are the first menu list entries all in order of increasing energy? Which entry corresponds to the thermal noise in an unpowered RC loop? What quantities would you add to the list?
one-gee constant proper-acceleration
Plot proper (traveler) and map times elapsed, as well as proper and coordinate speeds, as a function of map distance traveled for one acceleration-leg of a constant proper acceleration round trip.
historical and natural units for information
Note: Changes in Wolfram's widget-engine after the fact began obfuscating the simple log-relationship (s=k ln[W]) between bits, nats, & bans as well as J/K, with the result that the two widgets below were not working reliably. The problem may now have been fixed.
This first information units widget was inspired by the Information Storage Unit Converter widget, and allows conversion from a wide variety of information units including historical thermodynamic units like J/K.
bits of reciprocal temperature
The widget below calculates the coldness of the environment relative to the human basal value in natural units (about 175 ZB/Cal absolute) given the temperature in historical units (degrees Fahrenheit). This quantity relates to the information value of available work, as well as to the thermodynamic value of a cool place to dump excess heat. Just as the Fahrenheit scale was designed to go negative at the bottom range comfortable for human habitation, so this coldness scale goes negative near the top of that range.
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