Surprise is a -very- subjective thing. Is mathematical "information"
similarly subjective? (Cf. my note to Glenn about the "subjectivity" of
compressibility.)
--John
> -----Original Message-----
> From: owner-evolution@udomo.calvin.edu
> [mailto:owner-evolution@udomo.calvin.edu]On Behalf Of Brian D Harper
> Sent: Sunday, December 28, 1997 11:23 PM
> To: evolution@calvin.edu
> Subject: Re: ABCDEFGHIJKMNOPQRSTUVWXYZ
>
>
> At 10:13 PM 12/28/97 -0600, Glenn wrote:
>
> [...]
>
> >
> >Let me try to explain what all this means. Mathematics cannot determine
what
> >two people have decided. In information theory information is determined
> >not by what 2 people agree culturally or privately is information.
> >Information is measured by compressibility of the sequence. The alphabet
> >even minus the L has more information in it that does the sequence
> >isisisisisisisisis. This is highly compressible.
> >
>
> I'm really kicking myself that I didn't see Burgy's message.
> I noticed the L was missing and even said to myself no L,
> but didn't make the connection. Interestingly, I did see
> the theological twist James mentioned but figured this
> couldn't possibly be the hidden message Burgy was talking
> about :).
>
> Anyway, just wanted to say I'm in agreement with what Glenn
> has written. It's essential to understand that information
> theory does not address the meaning of a message. There's a
> simple reason for this. In designing a system for transmitting
> information one doesn't want the channel to be passing
> judgement on the transmitted message. The channel has to
> transmit all information even if its junk. This doesn't
> mean that the messages have no meaning, only that info
> theory doesn't judge whether messages are meaningful or
> not. Similarly, the genetic information system is also able
> to transmit meaningful as well as junk messages.
>
> When reading the newsgroup bionet.info-theory awhile back
> I came across a really useful suggestion for interpretting
> information content which I will apply to the present situation.
> The basic idea is to associate information with surprise.
> Imagine that you are receiving the message ABCD... one
> character at a time. The amount of information contained
> in the message can be roughly related to how surprised you
> are with each new character. Take Glenn's example. After
> receiving isis you are not surprised to see the next i and
> you become less and less surprised with each repeat of is.
> This is closely related to compressibility since your lack
> of surprise comes from having noticed a pattern. The existence
> of a pattern guarantees compressibility. One has to be careful
> here that the patterns one observes are structural patterns
> as opposed to patterns you might get by guessing the meaning
> of the message.
>
> Based on the above I would argue that the sequence ABCD...
> contains little information since it is an ordered pattern.
> After ABCDEF we would not be too surprised to see a G pop
> out next. But after ABCDEFGHIJK we are really really expecting
> to see an L. When M arrives instead we are surprised and begin
> to doubt the pattern we thought we saw. After MNOPQR the
> pattern re-establishes itself and we start to anticipate the
> next charater. Thus, I would say Burgy's sequence had more
> information than had he simply typed the entire alphabet
> without missing a character.
>
> Brian Harper
> Associate Professor
> Applied Mechanics
> The Ohio State University
>
> "... we have learned from much experience that all
> philosophical intuitions about what nature is going
> to do fail." -- Richard Feynman
>
>