Quantities of Information
Information theory is based on probability theory and statistics. The most important quantities of information are entropy, the information in a random variable, and mutual information, the amount of information in common between two random variables. The former quantity indicates how easily message data can be compressed while the latter can be used to find the communication rate across a channel.
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, which is based on the natural logarithm, and the hartley, which is based on the common logarithm.
In what follows, an expression of the form is considered by convention to be equal to zero whenever This is justified because for any logarithmic base.
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Famous quotes containing the words quantities of, quantities and/or information:
“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)
“In the information age, you don’t teach philosophy as they did after feudalism. You perform it. If Aristotle were alive today he’d have a talk show.”
—Timothy Leary (b. 1920)