> What is the difference between a random sequence of bits and a
> meaningful message? The correct decryption scheme.
That's an excellent question. I suspect a scheme might not be
necessary to infer the presence of meaning, but what I'm going to say
is very empirical.
Suppose a message m_n, of length n, which is a string of bits (e.g
m_8=10101010, with m_1=1, m_2=10, and so on)
Suppose a function f that takes a message m_n and predicts m_n+1
Suppose a learning algorithm L, such that L(m_n) = f. Let's assume
this algorithm does the best possible job (I know it's a stretch).
Now, for any length n of message m, we can obtain an f and then
measure the accuracy of f at predicting m_n at any n. We can then
measure the accuracy of this function, let's call that a.
So a is in [0.5, 1]
If a=0.5 the message is pure noise. If a=1 the message is completely
predictable, because every bit will always be a function of the
My empirical suspicion is that there is some range of a, between these
extremes, where meaning lives. Something akin to what people in
complex systems refer to as "the edge of chaos".
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