Re: Linford's Fallacy

The entropy of a binary sequence A_k is sum(A_k)/N.


In fact to be more related to the idea of entropy we would probably want to
define this as something more resonable(something symmetric):

sum(ln(1 + |A_k - A_(k+1)|))

This way the entropy of the sequence of all heads or all tails is 0. All
other sequences have larger entropy.

The sequences with alternating elements(010101... and 1010101...) are the
ones with the most "entropy".

Alternatively one could think of the binary sequences as the decimal digits
of a binary number. In this case 00000... and 11111.... are special. They
would be equal to 0 and 1 in base 10 which we do consider special.

So, while you can say that any natural number is just as special as any
other we do tend to treat 0 and 1 as special. In fact we need 2 elements to
be special to do algebra. 0 is the additive identity and 1 is the
multiplicative identity. We could have called them whatever we wanted but we
have to designate 2 and only 2 such numbers for a field. They are "special"
in that they were chosen... even if they were chosen at random.






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