Dear Sung,

You wrote:
> I think the main reason that we express 'information'  as a logarithmic
function of the number of choices available, n, may be because the human
brain finds it easier to remember (and communicate and reason with)  10
than  10000000000, or 100 than 1000000000. . . . 00000, etc.

No, this is not the reason.
The correct answer is that Shannon assume the n=0 as possible !!!
Because of this, to avoid dividing by zero he used log(s).
But this is impossible and many years the world works with log(s) not
understanding why !

log(s) is(are) no needed.

It is more clear and easy to work without log(s) :=)

Friendly greetings

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