可以查到起源是香农(Shannon)的"通信中的数学理论" (A mathematical Theroy of Communication)
香农在**开始的时候就使用三点说明了为什么要使用对数
The logarithmic measure is more convenient for various reasons:
1. It is practically more useful. Parameters of engineering importance
such as time, bandwidth, number of relays, etc., tend to vary linearly with
the logarithm of the number of possibilities. For example, adding one relay
to a group doubles the number of possible states of the relays. It adds 1
to the base 2 logarithm of this number. Doubling the time roughly squares
the number of possible messages, or doubles the logarithm, etc.
2. It is nearer to our intuitive feeling as to the proper measure. This is
closely related to (1) since we intuitively measure entities by linear comparison
with common standards. One feels, for example, that two punched
cards should have twice the capacity of one for information storage, and two
identical channels twice the capacity of one for transmitting information.
3. It is mathematically more suitable. Many of the limiting operations
are simple in terms of the logarithm but would require clumsy restatement in
terms of the number of possibilities. |
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