The mathematical theory of information is based on probability theory and statistics, and measures information with several quantities of information. The choice of logarithmic base in the following formulae determines the unit of information entropy that is used. The most common unit of information is the bit, based on the binary logarithm. Other units include the nat, based on the natural logarithm, and the hartley, based on the base 10 or common logarithm.
In what follows, an expression of the form is considered by convention to be equal to zero whenever p is zero. This is justified because for any logarithmic base.
Read more about Quantities Of Information: Self-information, Entropy, Joint Entropy, Conditional Entropy (equivocation), Kullback–Leibler Divergence (information Gain), Mutual Information (transinformation), Differential Entropy
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“The Walrus and the Carpenter
Were walking close at hand:
They wept like anything to see
Such quantities of sand:
“If this were only cleared away,”
They said, “it would be grand!”
“If seven maids with seven mops
Swept it for half a year,
Do you suppose,” the Walrus said,
“That they could get it clear?”
“I doubt it,” said the Carpenter,
And shed a bitter tear.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“The Walrus and the Carpenter
Were walking close at hand:
They wept like anything to see
Such quantities of sand:
“If this were only cleared away,”
They said, “it would be grand!”
“If seven maids with seven mops
Swept it for half a year,
Do you suppose,” the Walrus said,
“That they could get it clear?”
“I doubt it,” said the Carpenter,
And shed a bitter tear.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“English literature is a kind of training in social ethics.... English trains you to handle a body of information in a way that is conducive to action.”
—Marilyn Butler (b. 1937)