and variety are central to my critique of 'it from bit'. For we can only talk meaningfully about a thing, including a '', if it has distinguishing attributes. The way that they are knit together, as in the taste, shape and colour of an apple, defines the structure of the thing.

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.

Share Your Favorite Quotes

Know a quote that's missing? Help grow our collection.

Einstein... revealed... extraordinary things... [H]is space and time seem to be knit together in a way you can't pull them apart... [S]omeone moving relative to me at any speed would... divide space and time in different ways... [T]he huge excitement about simultaneity meant that the... issue of duration has... been forgotten...

Greek astronomers observed intricate motions of the sun, moon, and planets on the two-dimensional sky. They explained them—saved the appearances—by positing simple regular motions... in three dimensions. The success... [was] brought to a triumphant conclusion by Kepler...