owner-csound-outgoing wrote
>From owner-csound-outgoing Tue Aug  5 14:34:43 1997
From: owner-csound-outgoing
Date: Tue, 5 Aug 97 14:34:43 GMT
Message-Id: <2537.9708051434@maths.exeter.ac.uk>
To: owner-csound-outgoing
Subject: BOUNCE Csound: Non-member submission from [mogambo@real.net.au (Arne Hanna)]

>From mogambo@real.net.au Tue Aug  5 15:34:39 1997 remote from 
Received: from hermes.ex.ac.uk by maths.exeter.ac.uk; Tue, 5 Aug 97 15:34:39 +0100
Received: from root@december.real.net.au [203.25.56.1] by hermes via ESMTP (PAA13744); Tue, 5 Aug 1997 15:34:32 +0100
Received: from [203.17.243.73] (syd-pm1-8.real.net.au [203.17.243.73]) by december.real.net.au (8.6.12/8.6.9) with SMTP id AAA03937 for ; Wed, 6 Aug 1997 00:35:05 +1000
Message-Id: 
Mime-Version: 1.0
Content-Type: text/plain; charset=us-ascii
Date: Wed, 6 Aug 1997 00:35:04 +1000
To: csound
From: mogambo@real.net.au (Arne Hanna)
Subject: Formalized Music page 86

Sorry for diverging, but near the bottom of page 86 of the Pendragon
revised edition of Xenakis' book, we have:
the probability of X (a) remaining X  is .85, (b) changing to Y, is .15
the probability of Y (a) changing to X is .4, (b) remaining Y, is .6

"The entropy of the states of X will be -0.85 log 0.85 - 0.15 log 0.15 =
0.611 bits..."

I've gone over this many times, but no matter what I do, I don't get
anything like .611.  If anyone could shed any light on this, I'd be
grateful.  Apologies for being way off, but I don't know where else to ask.
Cheers
Arne


"Music is the weapon of the future"
                               Fela Kuti




-- 
James Andrews, maths CDO, ext.3977

>Date: Wed, 6 Aug 1997 00:35:04 +1000
>To: csound
>From: mogambo@real.net.au (Arne Hanna)
>Subject: Formalized Music page 86
>
>Sorry for diverging, but near the bottom of page 86 of the Pendragon
>revised edition of Xenakis' book, we have:
>the probability of X (a) remaining X  is .85, (b) changing to Y, is .15
>the probability of Y (a) changing to X is .4, (b) remaining Y, is .6
>
>"The entropy of the states of X will be -0.85 log 0.85 - 0.15 log 0.15 =
>0.611 bits..."
>
>I've gone over this many times, but no matter what I do, I don't get
>anything like .611.  If anyone could shed any light on this, I'd be
>grateful.  Apologies for being way off, but I don't know where else to ask.
>Cheers
>Arne

Hi,

After a touch of digging around through some information theory notes (plus
a nostalgic look through _The Mathematical Theory of Communication_  by
Shannon and Weaver), I found that you need to take those logs base 2. Or,
just take the base 10 figure you got and divide by log(2)=.301

 (-.85 log (.85) - .15 log (.15))/.301 = (.060 + .124)/ .301 = .611 bits


Happy entropy!


Dan Hosken
dwhosken@alum.mit.edu
dwhosken@students.wisc.edu

Computer Music Studio
Composition Department
School of Music
University of Wisconsin-Madison