Information theory would never have got off the ground if structured things—configurations—did not exist. - Julian Barbour

The concepts of message and probability enable one, for a definite source of <math>N</math> messages, to define Shannon’s information. If <math>p_i,\quad i = 1, 2, ..., N</math>, is the relative probability of message <math>i</math> and <math>\log p_i</math> is its base-2 logarithm, then the information <math>I</math> of the given source is(1) <math>\quad I = - \sum_{k=1}^N p_i \log p_i</math>.The minus sign makes <math>I</math> positive because all probabilities, which are necessarily greater than or equal zero, are less than unity (their sum being<math>\textstyle \sum_{i}^N p_i = 1</math>, so that their logarithms are all negative.

[I]n 1898... Henri Poincaré wrote... "On the Measure of Time" and he said... there are two fundamental problems to do with time. One... with the definition of duration... What does it mean to say that a second today is the same... [H]e said there's another issue... [not] so widely recognized. ...[H]ow do you define simultaneity at spatially separated points?

[I]f you imagine two NOWs... there will be some difference between them, and if you work out some weighted average of all of that difference... you can call that... the amount of time between them. ...[T]his has nothing to do with some substance... It's just difference between those two things. ...[T]his is the quantity that is... being measured by my watch...