Sung,
Ashby has taken same pains to cast this example at a high level
of abstraction by way of drawing out the "bare bones" structure
of the situation, but we know the intended interpretation makes
D the source of "disturbances" arising from the environment and
R the regulator who has to counteract them to maintain the goal.
Skipping to your remark about information, it does seem to me
that R has to make different choices depending on what D does.
In effect, R is trying to cancel the variety that D creates.
On to the question of irreducibility ...
Just by way of a usage note, I have pretty much quit using
the term "triad" in careful discussions because it invites
too much confusion between triples of sets like (D, R, O)
and triples of individual elements like (1, α, b).
Careful discussions of irreducibility will require us to work
from explicit definitions and here it turns out that there are
several different notions of irreducibility in common use that
are often confounded with each other.
Looking to the case at hand, L ⊆ D × R × O is a triadic relation
consisting of 9 triples or "elementary triadic relations" in the
embedding set D × R × O that consists of 3 × 3 × 3 = 27 triples.
We could reasonably use the ratio 3/9 = 1/3 as one measure of
constraint, determination, information, selection, or "law"
involved in carving L from the uncarved block D × R × O.
If we prefer an additive measure, we could extract the exponents
from 3¹/3³ and use their difference as our measure of information
in passing from D × R × O to L. Peirce actually pulled this very
trick in some manuscripts I saw one time, getting a simple version
of our modern day logarithmic measure of information.
Well, I ran out of time and didn't get to the various notions
of irreducibility, but I will next time ...
Regards,
Jon
Hi Jon,
I agree that the set L = (D, R, O) is a triad but I don't think it
is an "irreducible triad" in the Peircean sense, because there is no
"communication" or "transfer of information" between D and R. In other
words, R's decision is not influenced by D's and hence no information flow
from D to R.
Am I correct in interpreting the Ashby table in this way ?
All the best.
Sung
On Tue, Oct 6, 2015 at 12:20 AM, Jon Awbrey <[email protected]> wrote:
Forgetfulness Of Purpose • 6
http://inquiryintoinquiry.com/2015/10/05/forgetfulness-of-purpose-%e2%80%a2-6/
Peircers,
Just enough time for an incidental observation.
Consider the table Ashby uses to describe his first example of a
regulation game.
Table 11/3/1
`````|```R```
`````|`α`β`γ`
=====|=======
```1`|`b`a`c`
D `2`|`a`c`b`
```3`|`c`b`a`
A table like that is a compact way of describing a triadic relation,
in this case a relation L ⊆ D × R × O whose triples are displayed
in the following relational data table.
D R O
=====
1 α b
1 β a
1 γ c
2 α a
2 β c
2 γ b
3 α c
3 β b
3 γ a
May you find food for thought, a late night snack on those tables.
Reference
=========
Ashby, W.R. (1956),
An Introduction to Cybernetics,
Chapman and Hall, London, UK. Republished
by Methuen and Company, London, UK, 1964.
http://pespmc1.vub.ac.be/books/IntroCyb.pdf
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