Dear Terry,
I was going to ask you a similar question, but Birger got ahead. Show me one design theory that can be mathematized. But before that, we have to settle on what is design, what is design theory, how a theory can be expressed in mathematical terms, and so forth.
It seems to me that you enter very boldly into a philosophy of science minefield and on top of that, you make very extreme statements. If you say that some design theories can be mathematically expressed, it might be easier to defend such a position.
I am a bit astonished that you take such an extreme positivist view. What you say is not new and not unheard of, but people try to stay away of it for several decades. Is there are resurgence of Positivism? My observations are that the Positivism has "softened" a lot under the pressure of the renaissance of the humanistic paradigms. What is going on here?
Best,
Lubomir
PS By the way, didn't we deviate a lot from your initial post? I don't think that the current situation is very productive and if we conveniently change the topic, it might be better.
-----Original Message-----
From: PhD-Design - This list is for discussion of PhD studies and related research in Design [mailto:[log in to unmask]] On Behalf Of Birger Sevaldson
Sent: Monday, March 10, 2014 5:13 AM
To: [log in to unmask]
Subject: Re: Design Theory
Dear Terry
Please show us one mathematically expressed design theory.
Best regards
Birger Sevaldson (PhD, MNIL)
Professor at Institute of Design
Oslo School of Architecture and Design
Norway
Phone (0047) 9118 9544
www.birger-sevaldson.no
www.systemsorienteddesign.net
www.ocean-designresearch.net
________________________________________
From: PhD-Design - This list is for discussion of PhD studies and related research in Design [[log in to unmask]] On Behalf Of Terence Love [[log in to unmask]]
Sent: 10 March 2014 08:49
To: [log in to unmask]
Subject: Re: Design Theory
Hi, Ken,
Again, you are conflating the two different ideas. you can't make a silk purse out of a sows ear. . . If the original word version of a theory doesn't provide a complete functional model of all aspects of design, then how would representing that same theory in mathematical terms do so?
E.g. '"Wicked problems" have a large number of solutions' can be transformed into mathematical notation into ' The number of entities in the solution set of the set of problems bounded by the following criteria tends towards a large number'.
Why would I expect the mathematical representation of this to be a working model of design activity? I don't get your logic. Goedel's is a different argument.
You could think of it slightly differently. If you gave me a word-based description of a motorcycle you had seen; the word-based descriptions could be equivalently be created as a visual-representation, as a sketch of the motorcycle; or the words or sketch could be represented (as above) in mathematical propositions. I'm at a loss as to why you think the words, sketch or mathematical representation would be a working motorbike.
descriptions result in
Rittel & Weber's wicked problem 'theory' is a their proposal for a collection of boundaries on the characteristics of the concept they have called 'wicked problem'. In that sense it has the characteristics of a definition not a theory. As you say, it's a set of theory-related
(theoretical) propositions. Propositions, though. In spite of their nature as parts of a definition, most of them don't define anything. The most that can be said is they are partial pointers. In some cases they are unrelated.
I'm happy to critique Rittel and Weber's propositions, andnd they are easy enough to represent in set terminology. It's value, however, will probably more that it will demonstrate they ain't a theory, nor do they make sense except perhaps as a political statement, or a proposal for avoiding responsibility.
But, lets take it from the top on Rittel and Weber's 10 comments on what they called 'wicked problems'
1. Means there's no definition here so what follows in the remaining 9 items is irrelevant. Non-sequitor.
2. Is simply confused language. *Activities* have stopping rules.
Creating solutions to problems have rules and boundaries. *Problems*, however, are simply problems. They don't go about stopping or starting.
Non-sequitor.
3. Means there is an undefined (good-bad) spectrum of optimisation criteria.
Weird - of course solutions are not 'true or false. Do you know ANY
*solutions* that are true or false, except in the realm of binary logic?.
4. Contradicts 3. In 3, Rittel and Weber have already said they are defining the success of a solution to a 'wicked problem' on the criteria of an undefined spectrum of good-bad. Regardless of it being undefined, they have indicated they are testing solutions against a criteria - which contradicts 4.
5. Apart from the faulty logic (confusion between creating the solution and the solution itself) , its true, less goes at getting things right means each attempt is more significant. This isn't really a major theory item.
6. Means there are lots of possible solutions (i.e. the set of possible solutions tends towards a large number) - the second part of 6 doesn't seem to make sense.
7. Each problem is different (is that unusual?) 8. All problems result from the outcomes of other problems. Is this unusual?
all events result from other events.
9. Its confused language with faulty logic but it seems to mean ' The outcomes resulting from prior events (that if R&W had been trying to create a solution to them, they would have called a wicked problem) can be explained in lots of ways. Is this not obvious?
10. The professional identifying the solutions is responsible. This is clearly untrue for most planners and designers. I've yet to see the costs of social problems from poor designs being charged against planners personal bank accounts.
So? Rittel and Webers collection of sentences and comments about wicked problems is a theory? It doesn't look like it to me. It doesn't have predictive power, it doesn't define, and it isn't coherent. It had value at the time to draw attention to some characteristics of planning decisions, but a theory - no.
Warm regards,
Terry
-----Original Message-----
From: [log in to unmask]
[mailto:[log in to unmask]] On Behalf Of Ken Friedman
Sent: Monday, 10 March 2014 2:32 PM
To: PHD-DESIGN PHD-DESIGN
Subject: Design Theory
Dear Terry,
Thanks for your reply.
Before offering the example you request, I'll state that there is no straw-man argument in my notes. If a theory meets the criteria you propose, it will permit a complete mathematically-based functional model of all aspects of design.
You make this statement about ALL theories in any discipline. Since the set of ALL design theories must incorporate the sub-set of those theories that model ANY design activity, the sub-set of ALL design theories will afford us a functional, mathematically rigorous model of all aspects of design. As I wrote, I do not think this is possible.
You wrote,
-snip-
1. All theories (any discipline) can be wholly and exactly represented as mathematical functions (this is the set of ALL theories regardless of valid, useful or not). The relevant mathematical functions are typically found in complex non-linear multivariable multidimensional spaces.
2. There are significant benefits in terms of validity and usefulness if theories are in the set represented by continuous well-behaved mathematical function.
3. If a theory cannot be represented by a well-behaved continuous mathematical function, this is an indication that the phenomena being theorised about needs representing in a different theoretical manner typically by more than one theory.
4. A simple test for whether a theory is represented by a well-behaved mathematical function (and hence is a 'good' theory) is whether the phenomena and the mathematical theories are free from discontinuities or singularities.
5. The existence of discontinuities and singularities in the mathematical space field that represents a theory indicates the need to represent phenomena on each side of the discontinuity or at the point of the singularity differently. That is, it indicates that what was previously one theory actually requires several theories of which the minimum number is
(n+m+1) where n is the number of discontinuities and m is the number of singularities.
6. The above applies to a single characteristic of a phenomenon. Where discontinuities and singularities occur at the same point in respect to multiple characteristics of the same phenomenon this indicates the presence of (n+m+1) different phenomena and the need for (n+m+1) different vector space fields (bodies of theory) to describe them).
Conceptual analysis, the work of Foucault and other theorists in realms of sociology, communications and design theory can each be seen as a sub-sets of the above.
-snip-
Now, as requested, I will give an example of a design theory that you feel cannot be represented mathematically, at least not in full - that is, I do not believe that it can be wholly and exactly represented as mathematical functions. Despite this, the theory I am about to put forward is one of the most important sets of theoretical propositions in design and design thinking. You have used it yourself, so I'd argue that it has to count as a theory of some kind.
These propositions meet my criteria for a theory: a model that illustrates or describes how something works by showing its elements in their dynamic relationship to one another. This is the dynamic demonstration of working elements in action as part of a structure.
The theory I put forward with the challenge that you wholly and exactly represent these statements as mathematical functions is Rittel and Weber's
(1973: -166) theory of the wicked problem:
"1. There is no definitive formulation of a wicked problem.
2. Wicked problems have no stopping rule.
3. Solutions to wicked problems are not true-or-false, but good-or-bad.
4. There is no immediate and no ultimate test of a solution to a wicked problem.
5. Every solution to a wicked problem is a 'one-shot operation'; because there is no opportunity to learn by trial-and-error, every attempt counts significantly.
6. Wicked problems do not have an enumerable (or an exhaustively
describable) set of potential solutions, nor is there a well-described set of permissible operations that may be incorporated into the plan.
7. Every wicked problem is essentially unique.
8. Every wicked problem can be considered to be a symptom of another problem.
9. The existence of a discrepancy representing a wicked problem can be explained in numerous ways. The choice of explanation determines the nature of the problem's resolution.
10. The planner has no right to be wrong."
Later, I hope to add a few comments on your note. In several debates, you have used a tactic in which you decline to answer a challenge directly.
Rather, you answer a question with a question, or you propose trading questions and answers.
Since you have asked for a design theory that I feel cannot be represented mathematically, I am starting with this.
There are other problems, however, with the notion that "all theories (any
discipline) can be wholly and exactly represented as mathematical functions." This is the shadow of the logical positivist program. Kurt Goedel (1931, 1962 [1931]) put an end to that program, and even to the idea that one can build all mathematical propositions that way.
For now, I'll be curious to see Rittel and Webber's theory of wicked problems - a model, as I've stated - "wholly and exactly represented as mathematical functions."
Best regards,
Ken
Ken Friedman, PhD, DSc (hc), FDRS | University Distinguished Professor | Swinburne University of Technology | Melbourne, Australia | University email [log in to unmask]<mailto:[log in to unmask]> | Private email [log in to unmask]<mailto:[log in to unmask]> | Mobile +61 404 830
462 | Academia Page http://swinburne.academia.edu/KenFriedman About Me Page http://about.me/ken_friedman
Guest Professor | College of Design and Innovation | Tongji University | Shanghai, China ||| Adjunct Professor | School of Creative Arts | James Cook University | Townsville, Australia
Reference
Goedel, K., 1931, "Ueber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I." Monatshefte fuer Mathematik Physik.
Vol. 38: 173-198.
Goedel, Kurt. 1962 (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Translated bv B. Meltzer. New York: Basic Books.
Rittel, Horst W J, and Melvin M. Webber. 1973. Policy Sciences, Vol. 4, (1973), 155- 169
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