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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