bits and binits

[Jeff Prothero <jsp@GLIA.BIOSTR.WASHINGTON.EDU>]

| Another issue on which I've been having a think.
| I agree with F. Baube[tm] that computer implementation shouldn't be part
| of the definition of a bit; it is, after all, a binary digit (etymologically
| too!), and was first used in communication theory. I propose we call it a
| truth-quantum: jetka'u.
Please note that the information-theoretic concept of a 'bit' is
quite unrelated to the computer science concept of a 'bit'.  Last
time I took a class which needed to discuss both, we used 'binit'
for 'binary digit' and 'bit' for the information-theoretic term.
(If it had been a CSci class, maybe CSci would have gotten 'bit' *grin*.)

An information-theoretic 'bit' is just enough information to settle
a yes-no question which has an a priori 50-50 probability of going
either way.  A computer-science 'bit' is any system with two stable
state, in essence.

The above being logically but not pragmatically sufficient to elucidate
the difference, let me add some examples:

A blank "100 megabyte"
hard disk has approximately one billion zero binits on it;  but it holds
zero bits of information, since you know a priori that all binits are
zero and learn nothing by examining any individual one of them.

Physics establishes a deep, fundamental connection between the entropy
and information content of a system, and hence a quantitative relationship
between bits and energy.  Bits have a meaning embedded in the nature of
our universe.  Binits are by comparison a rather arbitrary human
convention.  (Yes, one can argue that the ability to embed binary arithmetic
is a property of our universe, and why we expect any other technological
civilization to have discovered binary also.  But this is a very different
point.)

One binit is always sufficient to hold one bit of information, but one
binit actually holds one bit only in the limit of perfect compression
and such... in general, each binit will hold less than one bit.
(Precisely, a binit's information content is 1/log2(p) where p is the
a priori probability of the bit being found in it's current state, if
I'm not phasing out here.)

Every system and communication channel has a precise theoretical
bit-content/bit-rate: the number of binits needed to represent it
depend on the algorithms and conventions used to encode it.

Confusing bits and binits is in essence as great an error as
confusing a name with the object named...

Jeff