Real System Design Issues --

[joseph simpson]

If all system activities are divided into two modes:

  -- System discovery mode 

  -- System design mode...

Then most of my current work is focused in the system discovery area. Specifically focused on the discovery of system structure.

I would like to branch out more into the system design area with an effort to create a system description language (SDL).  The system design language is viewed as an open source, collaborative effort to produce a controlled natural language for use in the description and specification of industrial based systems, produced using current industrial processes.

Anyone have any ideas about places to start?

Anyone interested in working in this area?

Anyone know of anything like this that is underway at this time?

Take care, be good to yourself and have fun,

Joe

--

Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

[James Martin]

Joe,

There are many out there working on architecture description languages (ADLs), which might have some relevance to your interest in system description languages. You might also take a look at the ISO/IEC 42010 standard on architecture description. By the way, this standard is up for renewal next year. Your work in this area could help improve that document. 

en.wikipedia.org/wiki/Architecture_description_language

Architecture description languages (ADLs) are used in several disciplines: system engineering, software engineering, and enterprise modelling and engineering ...

‎Introduction - ‎History - ‎Characteristics - ‎Common concepts of architecture

www.sei.cmu.edu/library/assets/Survey_of_ADLs.pdf

by PC Clements - ‎Cited by 402 - ‎Related articles

Abstract. Architecture Description Languages (ADLs) are emerging as viable tools for formally representing the architectures of systems. While growing in ...

xADL - A Highly Extensible Architecture Description Language for ...

isr.uci.edu/projects/xarchuci/

xADL is an architecture description language (ADL) for software and systems developed by the Institute for Software Research at the University of California, ...

And so on...

Could you help me understand the distinction between design and description, like when you said: "create a system description language (SDL).  The system design language is..."?  Seems that you would also want to "describe" the system even when in system discovery mode.

Thanks,

James

Sent from my iPad

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[Hillary Sillitto]

Worth looking also at Dov Dori's recent work on 'object process modelling' which has led to an ISO standard and - I think - an open source tool to support it. Another interesting open source tool is Capella which Thales developed and then released into the open source community.

I wonder if the greatest value added at this point would be to bridge between these tools and the tools you have developed for handling ISM and design structure matrices.

Good luck and have fun!

Hillary

[Richard Martin]

Joe,

 

CEN/ISO 19440 Enterprise integration — Constructs for enterprise modelling, might be close to what you are seeking. I’ve attached a few extracts to give you an idea of the standard. If you have more interest, please contact me.

 

Hillary also mentioned Dori’s work on OPM. We just submitted the final draft for publication by ISO of a formal specification of OPM as a Publically Available Specification document. He has a website devoted to OPM at http://esml.iem.technion.ac.il/opm/.

 

Cheers,

Richard

--

[Jack Ring]

Did not see James Martin’s post.

I suggest that we use Warfield’s distinction of descriptive models vs. prescriptive models. 

The main difference being that descriptive models must be confirmed by comparing them to what exists, both components and emergent behaviors, whereas prescriptive models are hypotheses regarding likelihood of future effects when thee model is instantiated, deployed and activated. The latter deserves continuous, intense assessment of fitness for purpose (intended Effects).  Authors of both are well advised to apply George Friedman’s book, Constraint Theory. Regarding languages, there is no significant difference between the language necessary, sufficient and efficient for descriptive vs. prescriptive. The key criteria is that the models be directly executable and scenario driven.

[joseph simpson]

James:

Thanks for the information.

Your questions are:

"Could you help me understand the distinction between design and description, like when you said: "create a system description language (SDL)."

In this context, I am using system design to indicate activities associated with systems that do not yet exist or are unknown. System description is more about the human ability to correctly interpret the symbol set that describes the system.  The system could exist or not.

  The system design language is..."?  Seems that you would also want to "describe" the system even when in system discovery mode.

You are right.

System description applies to all types of systems, whether the system was discovered (solar system) or designed (car).

One of the design goals, associated with a system description language, is the alignment of a small set of system relation logical properties with specific types of system structure and description.

In the current work with the structural modeling project, the augmented model-exchange isomorphism (AMEI) was created to map standard groups of logical properties to English words, structured graphics and mathematical forms.

The AMEI contains 27 standard groups of logical terms.  As Kevin Dye pointed out, only a small subset of the standard groups are normally used in industrial system description.  About three (3) to six (6) standard groups were identified.  These logical groups need to have English language words associated with them to start the mapping from AMEI constructs to a controlled natural language.

Take care, be good to yourself and have fun,

Joe

[joseph simpson]

Hillary:

Excellent choice!

Dov's work is great and I have looked at it in a general way.  I stopped considering Dov's work when the patent issues became known to me.

There appears to be an unresolved conflict between the OPM patents and an open source approach.

If the OPM patents did not exist or if the technology was released under an open source license (like GPL 3) then I would be very interested in the OPM system.

Given the encumbered nature of the OPM technology, I have not given it any more effort. 

There are open source tools, like Topcased or PolarSys that provide standard interfaces to graphics engines.  

My current plan is to find and use open source tools or created the required open source tools.

Take care, be good to yourself and have fun,

Joe

[joseph simpson]

Richard:

Thanks for the information.

It is my understanding the OPM has patent issues and is not open source.

Therefore, I stopped considering OPM as a viable technology.

Take care, be good to yourself and have fun,

Joe

[joseph simpson]

Jack:

Great information and insights.

The structural modeling project activity has generated discussion about a number if issues.  One of the most interesting aspects of this discussion (for me anyway) is the discovery of a wide range of interpretations associated with seemly 'well defined' language constructs and ideas.

While performing the task of mapping natural language constructs to logical properties, Kevin Dye encountered some interesting  outcomes.

Take the natural language concept, 'is-part-of.'  

The concept, is-part-of is irreflexive.  A whole can not be part of itself.

The concept, is-part-of is asymmetric. Object A is part of object B, so object B is not part of object A.

The concept, is-part-of is transitive.  Object A is part of object B and object B is part of object C, therefore object A is part of object C.

Kevin researched a list of natural language terms where the is-part-of  relation logical properties may not hold. For example:

A thumb is part of a hand, a hand is part of a person, and the person is part of an orchestra.  We do not consider a thumb as part of an orchestra.  There is some level of decomposition that is inferred from context that limits the transitive property.  

All interesting information, that should be included in any system description language. 

Constraint theory is very important in considering a well formed set of mathematical equations.  

I think it is important to create a set of isomorphic transforms that describe the same system in formal prose and/or formal graphics and/or mathematics.

A small subset of English terms can be used to start this activity.  Terms associated with system structure may be applied in both the system discovery mode and the system design mode.

The plan is to take a few small steps at a time.

Take care, be good to yourself and have fun,

Joe

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[Jack Ring]

Joe, 

The is-part-of example is a classic case of <, and >, without considering the =. Also known as a logical error. 

Jack

[joseph simpson]

Jack:

Great point.....

The natural language term is ambiguous in an informal context.

In a formal context some conditions would need to be determined. If we allow a general subset, then equivalence is allowed.  If we only allow a proper subset then equivalence is not allowed.

These are exactly the issues that need to be addressed in the transition from informal natural language to formal language.  The ambiguity associated with natural language is highly constrained or eliminated using a formal language.

Language ambiguity may be a source of many types of system description errors.  Very few system engineering authors address system relations at the logical properties level.  Some authors that have addressed system relations at the logical property level appear to have created a logical paradox and/or error set.  Use the DSM work of Donald Steward, for example, where the natural language relationship 'precedes' is used to organize a system.

Steward assigns the logical properties of:

  -- reflexivity

  -- symmetry

  -- transitivity 

to the precedes natural language relationship in his transition from informal language to formal language.

This assignment of logical properties creates an equivalence operator that, as Steward points out:

      "Note that by definition each xi precedes itself..."

In this natural language case the transition to formal language allows logically absurd system configurations.

It makes no sense to say that events precede themselves in a natural language.  However, the formal language operations will be performed without complaint.

The key area, in my mind, that needs to be addressed is the creation of a proper isomorphic connection between the informal language and formal language.

A small number of logical property sets appears to be able to cover a wide range of natural language constructs.

[Richard Martin]

Jack and Joe,

 

Hmmm! I expect the insurer of the orchestra includes in the premium determination a provision for dealing with thumbs and other digits that render the player impaired – most instruments require well-functioning thumbs. Specifying the extent of transitivity necessarily “is part-of” modeling. Do reflexivity and symmetry possess the same kind of extent necessity?

 

Cheers,

Richard

[joseph simpson]

Richard..
To say the Orchestra broke it's thumb is a bit award.

[Jack Ring]

Tweeeet!

The cause-effect view is not an is-a-part-of view.

[joseph simpson]

Richard:

Lets try this again...

I was out moving around when I sent the last message, that I effectively garbled.

In natural language, to say "The orchestra broke its thumb." is an awkward statement.

"Do reflexivity and symmetry possess the same kind of extent necessity?"

Great question, I would say the answer is no.

Reflexivity involves only one individual.

Symmetry involves two individuals only.

Transitivity involves three (or more) individuals. 

Please see the attached document for further details.

"Specifying the extent of transitivity necessarily “is part-of” modeling."

Can you expand techniques used to specify the extent of transitivity?  This is an interesting subject.

Take care, and have fun,

Joe

[joseph simpson]

Jack...

How about the natural language statement, "The orchestra has a broken thumb." , a statement of fact.

To me, it is still an awkward statement.

Have fun,

Joe

[Jack Ring]

Simple. An innappropriate usage of the language. An Orchestra does not have thumbs. A Orchestra signifies a set, not a being. This is the same kind of multiple inheritance that uneducated programmers committed with object technology. 

[Richard Martin]

Joe,

 

But “I am processing a claim for a broken thumb of the orchestra.” is not so awkward. So, the insurance claim concerns a thumb that is part of a person that is part of an orchestra that is part of a policy for insurance. The context is insurance and therefore the transitivity extent is determined by that context.  The same parts, {thumb, person, orchestra} also appear in the performance context, which is why the insurance context probably exists – maybe that is what jack was eluding to as a cause-effect view.

 

I’ll need to think some more about reflexivity and symmetry.

 

Cheers,

Richard

[joseph simpson]

Jack:  

"An innappropriate usage of the language." 

 

That may be true.

But which language?

The formal language (mathematics) or the informal language (natural language).

As shown in the attached document, the systems scientist and/or systems engineer work in the area populated with both types of languages.

Take care and have fun,

Joe

[joseph simpson]

Richard:

Good point.

I am developing two concepts associated with the transitive logical property, that may be of value in the analysis of natural language statements.

The first concept is 'binding scope.'  Binding scope for the transitive property indicates how many links may be traversed before the logical property is no longer applicable to the connected object.  The minimum binding scope would be two links (three separate objects).  The maximum scope could be infinite, but this concept needs more thought.

The second concept is 'transitive routing."  Transitive routing is associated with relations that are not transitive or intransitive.  The current practice for graphing system connections is to not indicate the transitive link on the graph.  If the transitive link is included then the graphs become cluttered and unreadable very quickly.

In out AMEI work, see chars at:

http://systemsconcept.org/html/Content/smp_arc/docs/02_13_2015/AMEIv1_1.pdf

In our AMEI work we show the links to support the detailed discussion on non-transitive relations.  However, we only use four (4) nodes in our graphs, to keep the number of links manageable.  The routing of the logical relation transitive property is a very interesting concept that may have some benefits.  The concept still needs more work.

Because individual transitive links are not encoded in most structured graphs, the transitive property can not be determined by reading a structured graph.

Take care and have fun,

Joe

[joseph simpson]

Given the fact that only partial information about the logical properties associated with the system organizing relation is available in structured graphic and mathematics form, the formal prose section is needed to provide complete information about the logical properties.

The logical properties are needed to provide a mechanism to specifically identify the semantics of some natural language system organizing relations.

If the 'north-of' natural language system organizing relation is used then the logical properties are well known:

  Irreflexive (an object can not be north-of itself)

  Asymmetric (If A is north-of B, then B is not north-of A)

  Transitive (If A is north-of of B, and B is north-of C, then A is north-of C)

The logical properties of the north-of relation are well known and the specific relation is clear.

However, if the natural language relationship 'connected-to' is used, the logical properties associated with the relationship are ambiguous.   As we demonstrated in the AMEI chart set, connected-to may be used to represent any of the 27 logical property groups.  To clearly specify a specific configuration for the relationship, the logical properties for the configuration must be provided.

Take care, be good to yourself and have fun,

Joe

[Richard Martin]

Joe,

 

Comments inserted below.

 

Cheers,

Richard

 

From: syss...@googlegroups.com [mailto:syss...@googlegroups.com] On Behalf Of joseph simpson
Sent: Saturday, May 2, 2015 12:34 PM
To: Sys Sci
Subject: Re: [structural-modeling] Re: [SysSciWG] Real System Design Issues --

 

Given the fact that only partial information about the logical properties associated with the system organizing relation is available in structured graphic and mathematics form, the formal prose section is needed to provide complete information about the logical properties.

[rm] The extent of information available from structured graphic and mathematics form is not necessarily partial or any more partial than text regarding logical properties associated the system organizing relation. Text does provide ways of expression that can be more succinct while quite readable. We tend to be more comfortable about word meaning and sentence structure than about symbolic graphics and mathematical phrasing, and therefore most often resort to the familiar and retain the less familiar for, oddly enough, expressing the more abstract concepts for which the text becomes lengthy or requires a word or two we do not have at our command.

 

The logical properties are needed to provide a mechanism to specifically identify the semantics of some natural language system organizing relations.

[rm] Assuming the logic at hand is capable of expressing the semantics. Limits such as “up to isomorphism” can reduce expression ability of logical systems.

 

If the 'north-of' natural language system organizing relation is used then the logical properties are well known:

  Irreflexive (an object can not be north-of itself)

  Asymmetric (If A is north-of B, then B is not north-of A)

  Transitive (If A is north-of of B, and B is north-of C, then A is north-of C)

 

The logical properties of the north-of relation are well known and the specific relation is clear.

 

However, if the natural language relationship 'connected-to' is used, the logical properties associated with the relationship are ambiguous.   As we demonstrated in the AMEI chart set, connected-to may be used to represent any of the 27 logical property groups.  To clearly specify a specific configuration for the relationship, the logical properties for the configuration must be provided.

[rm] Ambiguity can be fit-for–purpose or can be a driver for further elaboration to resolve the ambiguity, which may produce several statements, some unambiguous and some still ambiguous. The purpose of the model dictates which is sufficient for a given situation.

 

[joseph simpson]

Richard:

Great insights and comments...

Please see the responses below:

"[rm] The extent of information available from structured graphic and mathematics form is not necessarily partial or any more partial than text regarding logical properties associated the system organizing relation."

Good catch.

An example AMEI chart is attached for reference.

In the attached AMEI structured graphic the transitive links are shown in green.  This is a non-standard method of directed graph presentation.  In standard, directed graph representations, the transitive links are not shown because they clutter a graph of a large size.

The reflexive and symmetric properties of the relation can be read directly from the structured graph.  You are right, the information associated with a structured graph is determined by the graphic type.  In most directed graphs the transitive links are not shown.

"Text does provide ways of expression that can be more succinct while quite readable. We tend to be more comfortable about word meaning and sentence structure than about symbolic graphics and mathematical phrasing, and therefore most often resort to the familiar and retain the less familiar for, oddly enough, expressing the more abstract concepts for which the text becomes lengthy or requires a word or two we do not have at our command."

Very true, but in this specific case, we are most concerned with the text that describes the formal logical properties associated with the organizing relation.  The goal of this exercise is to represent the system organizing relation in three isomorphic forms: prose, structured graphics and mathematics.  The scope of the prose statements are limited by this goal.

"[rm] Assuming the logic at hand is capable of expressing the semantics. Limits such as “up to isomorphism” can reduce expression ability of logical systems."

Very true, but in this specific case, we are focused on the logical properties of of a single system organizing relation.  A well defined and limited scope of application.  We developed the Abstract Relation Type (ART) to support the evaluation of the matrix types.  The expressive power of these forms are limited, but their expressive power may be increased as more research is completed.

"[rm] Ambiguity can be fit-for–purpose or can be a driver for further elaboration to resolve the ambiguity, which may produce several statements, some unambiguous and some still ambiguous. The purpose of the model dictates which is sufficient for a given situation."

"Spot on.. the ART form and the AMEI have sections for formal prose and informal prose.  Informal prose are required to address ambiguity and develop formal prose systems.  We separate and name these prose sections to clearly identify their nature and purpose.

One of the main areas of concern is the use of ambiguous terms in a formal context.  For example, using the natural language term, 'north-of' in gathering relational information about a set of cities is reasonably safe because of the commonly understood logical properties associated with this natural language relationship.

However, using the natural language term, 'connected-to' in the same type of process without further definition of the associated logical properties greatly limits the value of any logical and/or mathematical computations used in that process.  The computations can be executed, their value is suspect. 

Take care, be good to yourself and have fun,

Joe

[Lenard Troncale]

Richard and Joe,

This recent stream of comments and discussion reopens Janet's suggestion that work on Warfield's ISM as modernized and extended by you folks is actually very pertinent to and consistent with the "operators/relations" of the Linkage Proposition sets in research on Systems Processes Theory. I would note though that the operators used for ISM are usually derived from human conversations and discussion about human views of the human-defined system, while in Systems Processes Theory these operators are proposed to be isomorphic between human systems and most all natural systems. Some insist this difference is insurmountable (Ackoff and Warfield in many past discussions with me) but I do not think they are insurmountable at all, but that our current mind set has traditionally erroneously made them so because of our attachment to humanocentrism (anthropomorphism). We have to get beyond that mindset, based on hard evidence of course.

In any case, work on ISM is work on disciplining the "operators" for both ISM and SPT IMHO. SO whether or not Joe would entertain looking at the Linkage Proposition set for SPT given his disciplined focus on expanding ISM, I applaud and support their work which someday may come together with ours.

Len

<ORC_11.odp.png>

[joseph simpson]

Len:

Very interesting set of comments.

In my mind, Mary and I have been focusing in two distinct areas:

   -- Basic structural modeling

   -- System language dyad

A graphic of the system language dyad application is attached for reference.  We hope to carefully construct the foundations upon which the practice of Interactive Management (IM) and Interpretive Structural Modeling (IMS) may be further developed.

When Mary and I started on this journey, we held the initial view that the ISM work of Warfield had been developed in a consistent manner.  We  quickly discovered that our initial view was not the case.

The challenge then became, how to address this large body of work that uses common names, terms and processes but has widely varying methods, computational schemes and semantics.  Some of the adaptations of Warfield's ISM provided interesting and useful tools.  The adaptation by Hitchins is one example where ISM and other evaluation tools are organized around the binary matrix forms associated with these techniques.  Hitchins also introduced the use of evolutionary computation to the ISM and IM approaches.

We decided to create a structured approach to the expanded body of ISM work in an effort to increase its application and use.  The fundamental aspects that guide this structured approach are detailed in "A Science of Generic Design," developed by Warfield.  As shown in the language dyad graphic, the augmented model-exchange isomorphism, is focused on creating two well defined structured interfaces:

  - between natural language and mathematics

  - between mathematics and system description

These language constructs should be applicable to any type of system.  A key property of our work is the ability to refine and tailor a language set for a specific language interpreter.  Machine language interpreters understand one type of input, human interpreters understand a different type of input.  

The current approach should be applicable to any type of system.  Warfield did focus on structured deterministic system analytical approaches.  This is not surprising, given the fact that he did much of his calculations by hand.  The expansion of these basic techniques to evolutionary computation (EC) opened up the area non-deterministic system evaluation. EC techniques are based on vast computing power to search a large solution space for acceptable answers. 

At this time we are using the properties of symmetry as an indicator of which type of modeling technique to apply.  Please see attached graphic.

I am not familiar with your work, but as the structural modeling approach matures it should be applicable to any type of system.  That is the goal anyway.

Thanks for the encouragement, maybe we can discuss the different approaches some time in July or August.  I am swamped until then.

[joseph simpson]

I forgot the symmetry graphic.. see attached

[Lenard Troncale]

Joe,

I realize you do not want to get enmeshed in a long set of streams of msgs. But FWIW, the following phrases you use to describe your work goals are completely similar for describing what we are doing in Systems Processes Theory .......

• For example, our Linkage Propositions are usually, but not always System language dyads
• Our work is between natural language and system description tho' we posit that it could be expressed in math
• Our work also should be applicable to any type of system
• Our work should also be understandable to a language interpreter like Prolog but not directly machine language
• SPT work should also be  applicable to any type of system.  That is the goal anyway.

So there must be some relation and synergy as Janet has suggested. However, I am quite suspicious and skeptical. Warfield focused on social systems management problems it seems to me. Those dyads are expressed in social systems domain specific language. Our dyads are expressed in domain-independent language many levels of abstraction from the specific. It is pure abstracted processes. But then mathematics (even as used in ISM) is a domain-independent language (in that it is also abstracted from numerous possible applications). Another interesting dissonance is the way you use symmetry; it is quite different from the way we use symmetry altho' I would consider yours a specific application of symmetry of logical relations and consistent with ours which is used in the generic or isomorphic manner.

I am also swamped with deadlines. Perhaps we will find ourselves answering the same deadline in the Fall.

Len

P.S. You added the symmetry graphic in a subsequent msg. But it seems you also mention a graphic of the systems language dyad applications. Are they one and the same?

<langDyad.png>

[Janet Singer]

Len,

The work Joe is doing is at the mathematical and therefore most abstract and domain-independent level. He is also writing software that can be used to support users building models in their domains of interest, starting from initial considerations of factors and relations of interest through efforts to pin down something that is sufficiently well defined that it can be mathematized, to manipulations of the mathematical model to identify and represent structural patterns in what the user entered. 

The software and mathematical methods are independent of, and customizable to, a user's domain. The same model-building steps are relevant no matter what domain is being addressed, from natural science to social systems intervention to literary analysis. 

The reason Warfield's method happens to be relevant to your work is that it provides excellent structured support and record-keeping for all the stages of model building, from initial idea generation on through successive refinements. Warfield saw that this process was needed to bring discipline and structure to the group modeling efforts he was engaged in.

But it is also useful for the group modeling work that you and cohort have been carrying out trying to identify whether you have identified the proper spanning set of systems process patterns; whether some patterns should be combined, nested, split, added, or dropped; what the candidate linkage propositions reveal about the selected patterns, etc., etc.

If you had been using Joe's software throughout this development work you'd have been building a rich database reflecting the progress of the effort. I hope that can begin soon —preferably at the IS in Seattle!

Does that help make the synergy in your projects a little clearer?

Janet

[joseph simpson]

Len:

The last messages referred to two specific graphics.  I just checked and they are still available for download on the previous messages in this email thread.  If you can not access them let me know and I will send you copies.

You are probably right about the activity level.

You know what they say, "If you want something done assign the task to a busy person."

Mary and I are working from a foundation built on a small set of system principles.  In general these principles are:

- A system is a relationship mapped over a non-empty set of objects.

- All real systems have a finite number of objects.

- All mathematical relations have a small set of organizing logical properties.

The Hilbert's language dyad as applied by Warfield is useful in addressing the communication issues associated with the understanding of large-scale systems.

In general, natural language relationships (informal language) are used to gather empirical information about the relationship that creates the system of interest.  Then, these informal relationship statements are transformed into formal a set of mathematical relations.

A key challenge is the proper alignment of the transformation from informal language (natural language) to formal language (mathematics).  Our work with the augmented model-exchange isomorphism (AMEI) is an attempt to create a standard well-known set of logical property grouping that may be used in transformation from natural language to formal language.

Natural language (informal language) has its advantages.

Mathematics (formal language) has its advantages.

In my opinion, system scientists and engineers must be able to validate the transformation process in some fashion.  

We have identified cases where the transformation from informal language to formal language is just bogus.  It would be hilarious if people did not get so upset about the issue.  

If we can achieve a focus on the informal language to formal language transformation process that contains a well-defined validation process, then I believe we will have made a substantial contribution.

In our presentations at INCOSE in July I will discuss some of the more advanced processes proposed by Warfield.  

We have identified the system organizing relation logical property of symmetry as a candidate discriminator in the selection of system analysis methods.

If a system organizing relation has a asymmetric logical property then one type of system analysis methods and techniques are used.  These methods and techniques are usually deterministic.

If the system organizing relation does not have a asymmetric logical property then a different set of system methods and techniques are used.  These techniques are usually non-deterministic.

We are just trying to discover 'logical tags or markers' that indicate which general systems analysis approaches should be used in any given case.

The limited computing power available to individuals from Warfield's era did not support the application on non-deterministic methods like evolutionary computation.  Today, evolutionary computation is a very practical choice.

In fact, you can build your own super computer for a few thousand bucks these days..

Our use of symmetry is very practical and derived from the analysis of past practice.