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Topic: Multiplication Is Not Repeated Addition
Replies: 45   Last Post: Sep 30, 2010 7:11 AM

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Alain Schremmer

Posts: 865
Registered: 10/10/05
Re: Multiplication Is Not Repeated Addition
Posted: Apr 7, 2010 10:47 PM
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On Apr 7, 2010, at 9:02 PM, GS Chandy wrote:
> Background note ? What Is Modeling (Warfield's approach)
> ==================================
> D: A background note: What is modeling?
> -- By G.S. Chandy
>
> The Structural Modeling Approach ? and how it is significantly
> different from any conventional approach
>
> First, a quote from John N. Warfield:
> Modeling is a process that begins with human perception. A
> sequence of the following nature describes the activity of modeling:
>
> 1) Perception
> 2) Storage in the brain
> 3) Identifying a context within which to place the perceptions, and
> within which they can potentially be integrated
> 4) Generating factors associated with that context and with the
> perceptions that are the focus of attention at the time
> 5) Identifying types of relations that appear to be associated with
> these factors in the chosen context
> 6) Structuring the factors to show how they are interrelated
> through specific relationships that are representative of the
> selected types
> 7) Interpreting the structures produced
> 8) Associating the factors with algorithms that permit the
> relationships discovered to be quantified (if they are possible to
> quantify)
> 9) Assigning or computing numerical values to/for the factors
> 10) Interpreting the model-related information for purposes of
> design or decision-making
>
> (Above paraphrased from ?Structural Thinking?, J.N. Warfield:
> 1995-96 Essays on Complexity)
>
> The above sequence describes Structural Modeling, the process
> underlying Interactive Management (and the One Page Management
> System). Built into the above-outlined Structural Modeling
> process, when IM or OPMS is used, is an ongoing comparison of model-
> related information at each stage with the reality on the ground.
> These comparisons become sharper and more focused as the models
> evolve and develop over time.
>
> The conventional way (which the IM or OPMS process would not allow
> at all) is to start at Step 8 or at Step 9 of the above-outlined
> modeling sequence.
>
> In fact, most discussions between people not using IM/OPMS start
> out at Step 8 or Step 9, usually leaving out Steps 1 to 7, which
> are pre-requisite for clear understanding all round! (It is true
> that there are, on occasion, some context-clarifying remarks made,
> but these generally lack adequate focus to ensure truly clear
> understanding all round). Thus, many discussions between people
> are, in the conventional way, based on sets of ?mental models?
> that are significantly different from each other because of
> differing backgrounds of the people holding them. These mental
> models on which different people are basing their discussions are
> left entirely unclarified. Because of the differences in context,
> the very same words spoken by different people could often mean
> significantly different things. In any case, the context is
> entirely unclear. This leads to non-understanding,
> misunderstanding, confusion, and, finally, ineffective or
> incompetent action.
>
> We are interested in ensuring effective action at every level in
> the organisation ? starting with the individual. Because
> discussions in the Structural Modeling process are always based on
> a significant clarification of the context of each idea and thought
> contributed to the discussion by each person, subsequent action is
> much more likely to be effective. (Step 3 of the sequence of
> Structural Modeling outlined above).
>
> It should be observed that ?Structural Modeling? INCLUDES the
> ?conventional modeling process?. The conventional ?numerate
> models? (showing numbers, e.g. how much money, how many copies will
> be sold, and so on ? on which most people rely to the near-total
> exclusion of any structuring activity) will develop, in a natural
> way, as the structure of the interrelationships of various issues
> becomes clear. The difference is that the numbers developing
> through the Structural Modeling approach are based on a detailed
> consideration of all structural aspects of the issue, and will
> therefore have far higher reliability than the numbers made in the
> usual approach.


"Modeling" and "Model Theory" use the term "model" in rather
different, but not totally unrelated, senses.

In "model theory", given a structure, that is a set with various
subsets of various cartesian powers, and a sentence well-formed from
primitive terms, the structure is an interpretation of the sentence
if the various n-ary predicates correspond to the various subsets.
The interpretation is a model iff the sentence is true under that
interpretation.

For a few more details, see p.2 and ff at http://
www.freemathtexts.org/References/AMATYCReview/13-
ModelTheoreticalThinking.pdf

Regards
--schremmer












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Date Subject Author
2/19/10
Read Multiplication Is Not Repeated Addition
Jonathan Groves
2/20/10
Read Re: Multiplication Is Not Repeated Addition
Alain Schremmer
2/20/10
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2/22/10
Read Re: Multiplication Is Not Repeated Addition
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4/7/10
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4/11/10
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2/25/10
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