[PEIRCE-L] Re: Forgetfulness Of Purpose • 7

[Jon Awbrey]

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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inquiry list: http://stderr.org/pipermail/inquiry/
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Re: [PEIRCE-L] Re: Forgetfulness Of Purpose • 7

[Sungchul Ji]

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  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
>>
>>
> --
>
> academia: http://independent.academia.edu/JonAwbrey
> my word press blog: http://inquiryintoinquiry.com/
> inquiry list: http://stderr.org/pipermail/inquiry/
> isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
> oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
> facebook page: https://www.facebook.com/JonnyCache
>
>
> -
> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L
> but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the
> BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm
> .
>
>
>
>
>
>


-- 
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

www.conformon.net

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[PEIRCE-L] Re: Forgetfulness Of Purpose • 7

[Jon Awbrey]

Sung,

Thanks for those thoughts, which will take me a while to work through.
I'm sure I must be wrong about something somewhere but I won't be able
to tell what configuration or sample space is relevant to the problem
at hand until I get a good description of what exactly that problem is.

I think it's still a good question about the degree of “communication”
or “transfer of information” between D and R within G_1 and its bearing
on the irreducibility of G_1 as a triadic relation, so I'll put a marker
here and return to the question if and when I get a better handle on it.

At any rate, we can still investigate the irreducibility of G_1 --
I gave it a new name because there will be more examples coming --
independently of the information question, so I will turn to that.

Regards,

Jon

On 10/8/2015 5:02 PM, Sungchul Ji wrote:

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  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



--

academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache

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