From: toms@fcs260c2.ncifcrf.gov (Tom Schneider)
Newsgroups: bionet.info-theory
Subject: Re: Mead and Conway (Section 9.11)
Date: 6 Oct 92 17:04:25 GMT
Distribution: bionet
Organization: Frederick Cancer Research and Development Center

In article <1992Sep29.093739.12409@bnr.co.uk> pgh@bnr.co.uk (Peter Hamer) writes:

|Surely, in a fairly weak sense, entropy does have something to do with
|the observer, and their beliefs?
|
|* Entropy is defined as a function of probabilities.
|
|* These probabilities are assigned with respect to some hypothesis.
|
|* Hence entropy is not an absolute measure, but conditional on the
|  hypothesis used in assigning probabilities to events.
|
|* So the *measured* entropy change of a ribosome would differ between
|  observers holding different hypotheses.

 alist 4.30 aligned listing of:
 * 90/02/28 19:38:01, 82/08/19 22:48:00, ga: gene absolute begins -60 to +40, 3.03
 The book is from:   -60 to 40
 Alist list is from: -26 to 18

       -----------------                   +++++++++
       22222221111111111--------- +++++++++111111111
       654321098765432109876543210123456789012345678
       .............................................
     1 aattccattcctaggaggtttgacctgtgcgagcttttagtactc
     2 tagagccctcaaccggagtttgaagcatggcttctaactttactc
     3 taaggcaatgcaaggtctcctaaaagatggaaacccgattccctc
     4 cggccattcaaacatgaggattacccatgtcgaagacaacaaaga
     5 gtacttcactgagtataagaggacatatgcctaaattaccgcgtg
     6 cgttgaaactttgggtcaatttgatcatggcaaaattagagactg
     7 gtgcttagtaactaaggatgaaatgcatgtctaagacagcatctt
     8        aaatcttggaggcttttttatggttcgttcttattacc
     9 gttcaagattgctggaggcctccactatgaaatcgcgtagaggct
    10 gctgctaaaggtctaggagctaaagaatggaacaactcactaaaa
    11 gaagttaacactttcggatatttctgatgagtcgaaaaattatct
    12 aaatcgaagtggactgctggcggaaaatgagaaaattcgacctat
    13 gttcaaccactaataggtaagaaatcatgagtcaagttactgaac
    14 tcgtcgctgcgttgaggcttgcgtttatggtacgctggactttgt
    15 aaattacgtgcggaaggagtgatgtaatgtctaaaggtaaaaaac
    16 ttcggccccttacttgaggataaattatgtctaatattcaaactg
    17 taggttttctgcttaggagtttaatcatgtttcagacttttattt
    18 ctccagccacttaagtgaggtgatttatgtttggtgctattgctg
    19         atcaaacggaggcttttcatgtttaaagtacattctg
    20 gctcaaaaatcttggaggagtcaactatgaagtctcgacgtggct
    21 gccgtaaaaggcctagggaataaagaatggaacaattcactcaaa
    22 gaaattaacaagtacggatatttctgatgaaaccaaaaactacgt
    23 aaatcgaagtggactgctggtggaaaatgaggaaattcaatctca
    24 tgacacaaaccacaaaggaaactgaaatgtctaaatcaaacgaat
    25 tcgccgtgctatcgaggcttgcgtatatggaacactggactttgt
    26 cgtcttcacttttaaggagttatgtaatgaaaaaatcaattcgcc
    27 gtcccactctatttaaggatacaaaaatgtctaacgttcaaacat
    28 tactgcaaagccaaaaggactaacatatgttccagaaattcattt
    29 tcaacctctgaaataaggattatcctatgtttggctctatcgctg
    30 ttttctgattatcaaccggggtacatatgattgacatgctagttt
    31 tgtttaaagcatttgagggggattcaatgaatatttatgacgatt
    32 cttaaaatcgcataaggtaattcaaaatgattaaagttgaaatta
    33 tctgcgcctcgttccggctaagtaacatggagcaggtcgcggatt
    34 cttggtataatcgctgggggtcaaagatgagtgttttagtgtatt
    35 tttacccgtttaatggaaacttcctcatgaaaaagtctttagtcc
    36 agcctttttttttggagattttcaacgtgaaaaaattattattcg
    37 atactgcgtaataaggagtcttaatcatgccagttcttttgggta
    38 tcttatttggattgggataaataaatatggctgtttattttgtaa
    39 tgtttcaattaaaaaaggtaattcaaatgaaattgttaaatgtaa
    40 ttgcgtgtaattgcggagactttgcgatgtacttgacacttcagg
    41 aggtggccttttgaagaggatcagaaatgggaagaaggcgaagtc
    42 caaagctaactgacaggagaatccagatggatgcacaaacacgcc
    43 atcccttgcggtgatagatttaacgtatgagcacaaaaaagaaac
    44         atgtactaaggaggttgtatggaacaacgcataaccc
    45 attgttatctaaggaaatacttacatatggttcgtgcaaacaaac
    46 tactggatctatcaacaggagtcattatgacaaatacagcaaaaa
    47 gcccttgcggcctaataaggaaaattatgtacaatattaaatgcc
    48 cccgaccaagaacaagaggatttttaatggaaggtttaattgaag
    49 ccttctataaatacttaggaggtattatgaatatatttgaaatgt
    50 ctaattaaaatatttaaaggaaacatatgaaaacatatcaagaat

These are ribosome binding sites from E. coli.  Anybody could make such a
collection by using modern molecular biology methods.  The are aligned at the
start point for translation.  This could be confirmed in every case by protein
sequencing.  Hence the data set is independent of any particular human
observer.  Now consider the frequencies of bases at each position.  Now either
gather such a large set that errors are tiny, or assume that frequencies
approach the probabilities.  There are your probabilities.  Hence the
uncertainty of the binding sites (NOT THE ENTROPY!!!!) is measurable without
humans and so is independent of them.  The maximum entropy work is interesting
and useful, but this case demonstrates that something must be wrong if one
always is going to insist that probabilities are a human construction.

Looks like my postings and responses may be irregular for a few days as our
systems administrator is having some trouble switching our news reader to a new
machine.

  Tom Schneider
  National Cancer Institute
  Laboratory of Mathematical Biology
  Frederick, Maryland  21702-1201
  toms@ncifcrf.gov