Jon, lists,
(*1*) At
http://inquiryintoinquiry.com/2015/10/07/forgetfulness-of-purpose-%E2%80%A2-7/,
you wrote:
"Looking to the case at hand, [image: G_1 \subseteq D \times R \times O] is
a triadic relation consisting of [image: 9] triples in the larger set [image:
D \times R \times O] that consists of [image: 3 \times 3 \times 3 = 27]
triples."
It seems to me that the table at hand, although consisting of 9 triples, is
one of the 27 possible 3 x 3 tables (each having 9 triples) and hence
carries log_2 (27) = 4.75 bits of Shannon information (to be denoted as
I_S), if all the 27 tables have an equal probability of occurrence:
I_S = H1 - H2 = log_2(27) - log_2(1) = log_2
(27) = 4.75 bits
(1)
where H1 is the Shannon entropy of the table under discussion before
selection and H2 is that after selection by an agent carrying (or
implementing ) information, I_S.
(*2*) If the choices available to R, i.e., alpha, beta, and gamma, have
equal probability of being selected, then R will need log_2 (3) = 1.58 bits
of Shannon information to select the winning choice:
I_S = log_2(3) - log_2(1) = log_2(3) = 1.58 bits
(2)
(*3*) As you can see, Equations (1) and (2) clearly distinguish between
Shannon entropy, H, and Shannon information I_S. That is, I_S is not H.
This is the main content of what I recently called the First Law of
Quantitative Semiotics (FLQS) which may be more conveniently called the
First Law of Informatics (FLI). In words, FLI states that
"Information is not entropy, since information can be negative, positive or
zero but entropy cannot be negative." (3)
Statement (3) must be valid because entropy, either thermodynamic or
Shannon, cannot be negative according to the Third Law of thermodynamics in
the former case and by definition in the latter case,
(*4*) Applying FLI to the Ashby table under consideration, it may be
stated that the Ashby table carries 4.75 bits of information, and R can
exert 1.58 bits of control information when activated by the combination of
the information carried by D and the energy dissipation driving the
activities of D and R.
All the best.
Sung
On Thu, Oct 8, 2015 at 9:54 AM, Jon Awbrey <[email protected]> wrote:
> Sung, List,
>
> On 2nd or 3rd thought I think you are correct in saying that
> there is no correlation between D and R if we are looking at
> just those two factors. What I think I was thinking is that
> there is a correlation if we condition everything on getting
> a particular outcome.
>
> Regards,
>
> Jon
>
> On 10/7/2015 11:23 PM, Jon Awbrey wrote:
>
>> Forgetfulness Of Purpose • 7
>>
>> http://inquiryintoinquiry.com/2015/10/07/forgetfulness-of-purpose-%e2%80%a2-7/
>>
>> Sung, List,
>>
>> I went ahead and put a version of my last message on my blog --
>> it looks like Ashby's example is worth spending some care on
>> and I'll be able to do a better job of formatting the tables
>> and so on when I get down to discussing the various notions
>> of irreducibility. I won't bother copying the revised text
>> here as the content is pretty much the same, but just leave
>> the link above.
>>
>> Regards,
>>
>> Jon
>>
>>
> --
>
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--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
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