Dear Terry,
I respect your contributions to design research and to this discussion lists. You help us keep the debates at scholarly level and bring a lot of new information. However, I believe that it might be useful to bring a more realistic look at mathematics.
There is an adage about survey research: garbage in, garbage out. The same is true about the use of mathematical models. Math by itself would not help you model the world. Math will help you only if you have theoretical models of the world (if this is possible at all). If your theoretical models are wrong, math will take you further in the wrong direction. You know that each disciplinary model is an approximation and carries a lot of biases and errors. The math constructions that translate disciplinary models into mathematical language are also approximation of processes going on in the real world. These math models come with their own approximations and generate huge deviations from the original disciplinary models. You know the adage "lost in translation."
You are wright to talk about new mathematical models. Current math can be applied mostly to some physical processes that display linear or planar patterns of behavior. In complex areas like meteorology, this math is absolutely useless. There are attempts to use new math models there, like catastrophe theory. If we move to the social sciences, even the catastrophe theory is incapable to help. The complexities are difficult to be rendered in theories, and impossible to be expressed mathematically. Everyone who is talking to you about mathematical models in the social sciences is either referring to stochastic processes in society or is simplifying the social reality to the level that it becomes linear.
So, it is a long way to producing somewhat relevant theoretical models. It is a long way to producing mathematical models/languages that can match the complexity of social phenomena. (I exclude mass phenomena here.)
You mention that you have engineering background. As an engineer you know that there are several competing theoretical models for the behavior of the same structures and materials. In different countries/cultures they use different theoretical models for that purpose. I was quite surprised when I learned about that as a student. It looks like the physical world is frozen in time and we know everything about it, but in different cultures we see it very differently and come to different explanations about its behavior and outcomes. After we select one theoretical model, we have several options for mathematical translation. This brings another level of deviations. At the end, the formulas that I have seen in civil engineering, might be very different depending on scientific culture and theoretical and mathematical beliefs.
Now let's talk about teaching math to engineers so that they can calculate building structures. Math is a good device to develop human logic and abstract thinking. However, engineers today just enter data in computer programs. They are not stimulated to develop their own software because the calculation methods need to be approved, the software needs to be approved, and so forth. It is not like taking the math textbook and inventing new calculation methods and making new software. I have the perception (I might be wrong) that today's engineers use less math then 50 years ago. Do you remember the time of the slide rule; the hand-held calculators with the formulas? Now they are so obsolete. You don't need to know math to calculate your structures. You need to know where to enter your data in the boxes of the computer interface. (I simplify.)
The big problem is that engineers don't have motivation to study math, the society doesn't have incentive to teach math, and the question is who is going to develop the next generation mathematical models for physicists and engineers. That is the problem. Because, in order to develop a few hundreds of geniuses who will invent the new mathematical models, we need to teach math to millions of engineers with the hope that some of them will develop the critical mass of motivation and knowledge to produce new calculation methods. That is how I see the use of math and the need for math in engineering education.
Now when we go to architectural design, forget about math. You can't do much with math there. Someone might tell you that they developed planning software. This is actually a spreadsheet for entering information about rooms, sizes, and adjacencies. The software is diagramming the simplest relationships (adjacencies) and producing adjacency diagrams. Human beings are revising them and changing them substantially, because, as I mention above, it is garbage in, garbage out. So much about math in architecture. Actually, if you want to be a good architect, you need to be a good philosopher and sociologist, anthropologist and psychologists, not a mathematician. The space budget is about arithmetics. Fourth grade. Period. And even the production of the adjacencies diagrams is not rocket science. The conceptualization of spatial experiences is rocket science (in architecture).
Consider that typical design curriculum is about 160 credit hours till getting a Master's degree. These are 55 courses. Deduct 20 general education courses. You get 35 courses. Actually less, because the studios are very often at 6 credit hours. So, can you teach all the complexities in the world in 30 courses? And can you put 10,000 hours for studying math? In these 30 courses, students pout about 30 x 100=3,000 hours. And basically they learn something about a small number of topics. What you are propagating is a work for superbeings. And even they may not be able to master all the theoretical models and all the math so that at the end of the day, they can select a relevant theoretical model, then find a math model that approximates the trajectory of the phenomenon that they model, and then they start calculating.
Terry, appreciations for your contributions and your role to periodically revisit simple truths and complex realities!
Best wishes,
Lubomir
Lubomir Popov, PhD
Bowling Green State University
Bowling Green, Ohio, U.S.A.
-----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 Terence Love
Sent: Saturday, May 03, 2014 3:54 AM
To: [log in to unmask]
Subject: Re: Ten Thousand Hours for Expertise
Hi Ken,
Apologies about the delay in responding to your earlier posts.
Some significant developments here are talking up all of my time at the moment.
I'll reply fully as soon as I've some decent amount of free time.
In the meantime, a quick response.
There are ways of teaching mathematics fast. My experience is pretty well everyone is capable of doing maths at a high level. Most people's maths development has been temporarily blocked because of missing elements in their early maths education. The sequential nature of maths learning means later study became impossible.
Second, the same concepts (in terms of epistemological structure) relating to all aspects of a field apply across all disciplines. This makes learning multiple disciplines in short time possible. Maths is helpful to provide a shorthand code for universalising concepts.
Together these cut the need for multiple amounts of 10,000 hour blocks
Think of the proposal for maths being increasingly of benefit in design as being like suggesting in the 1950s that industrial art would in the future be predominately done by computers and hence design schools will have to teach industrial artists how to use software. Some at the time would be arguing about removing elements from the curriculum like sizing and stretching paper, grinding inks and paints, developing complex curves by rules, and other conventional art skills on which industrial design of that time depended (and have since mostly disappeared from graphic design courses). Some would be arguing there would only a few that would be capable of it. Some would argue that only a few would be needed.
Best regards,
Terry
-----Original Message-----
From: [log in to unmask]
[mailto:[log in to unmask]] On Behalf Of Ken Friedman
Sent: Saturday, 3 May 2014 3:07 PM
To: PHD-DESIGN PHD-DESIGN
Subject: Ten Thousand Hours for Expertise
Dear All,
My questions to Terry on mathematical expertise for designers have had me thinking further. Two specific issues rank high.
First, where are we to get design students with a sufficient foundation in mathematics to move from competence to mastery?
This is not a case of finding students who are preparing for careers in theoretical or applied mathematics, or in fields that require these skills, for example, physics, engineering, actuarial science, or some branches of psychology. These people are developing the foundations they need to move from competence to mastery in mathematics.
Here, we are talking about design students. These people are developing foundations in the skills they need to move from competence to mastery in design. It is from this cohort that we would need to find students who are ALSO developing the foundations they need to move from competence to mastery in mathematics. If they do not arrive at university with a high level of competence, they will not achieve the kinds of mathematical fluency that Terry (2014) describes, a capacity for "mastering abstraction and meta-abstraction along with predicting dynamic behaviors in multi-dimensional spaces, going beyond linear four-dimensional understanding of the world, understanding and using limits and disjoints, moving between discrete and continuous, combinatorics and design theory (different from what is known as design theory in the design industry), understanding the calculus of change and feedback, and moving between set and metrological mapping of concepts."
Second, assuming that we can find students with foundations for both sets of skills, how are we to find time within the design curriculum to bring students to MASTERY in both?
There is an extensive amount of research on the time that human beings require to move from competence to mastery in any field. Innate talent and possible genius aside, the rule of thumb is roughly ten thousand hours or roughly ten years of deliberate, reflective practice.
Anders Ericsson and his colleagues did the key research in the 1990s (Ericsson, Krampe, and Tesch-Romer 1993; Ericsson, and Chamess 1994; Ericsson and Lehmann 1996).
Those who wish to read these articles will find them on my Academia page in the "Teaching Notes" section:
https://swinburne.academia.edu/KenFriedman
These will be available through Saturday, May 10.
For those who wish to read more deeply, Ericsson (1996) edited an excellent book of research papers on these issues. There have also been several good popular books on these topics by Geoffrey Colvin (2008), Malcolm Gladwell (2008), Daniel Coyle (2009), and Matthew Syed (2010).
What we know about human learning suggests that we cannot find enough talented students to fill out more than one or two entry cohorts a year on a worldwide basis. The size of these cohorts is likely to be so small that there would be no need for more than one or two university programs to accommodate them.
However, there is also the question of financing. Today's educational framework is complex and available funding has shrunk greatly in recent years. Given the current context, could even two universities afford to fund the resources needed for a full dual program in both mathematics and design as linked sets of skills?
There is also the question of staffing. Teachers in any such program would themselves need special skills. Even though the teachers might not themselves have dual skill sets, they would need high levels of interdisciplinary capacity to work with students whose projects take them across disciplinary boundaries that the teachers might not themselves move across. These teachers would need a great deal of methodological sensitivity, and a capacity to work comfortably in interdisciplinary teams with the other teachers.
Given this, I can't imagine more than a handful of elite design schools based in strong research universities with the capacity to develop and manage such programs.
Even without the demand for high-level expertise in mathematics, our field faces significant challenges in developing robust research programs in design at the graduate level. On a worldwide basis, I estimate that fewer than fifty design schools offer truly robust research programs.
When it comes to mathematics, we can gauge some of the problems by comparing this with the one kind of design program that requires genuine working skills in mathematics: product design engineering. Worldwide, we only half a dozen programs graduate full-fledged product designers who are also accredited engineers. These product design engineers have a high level of working skill in mathematics, but not the level of skill for expressive mathematics that Terry describes. In my view, the challenges of a program that would train designers to the level of fluent mathematical mastery that Terry proposes are nearly insurmountable.
Before returning yet again to this debate, I'd be happy to see anyone whatsoever give answers to five questions.
(1) Are these skills important for ALL designers? If so, why? If not, why?
(2) If these skills are not important for all designers, for which designers are these skills important? Why?
(3) Let us assume that this level of mathematical skill is important for some group of designers, no matter how small. How are we to locate appropriate cohorts of students who have the background required for mastery in BOTH design and mathematics? Does anyone have an estimate of the size of these cohorts on a worldwide basis?
(4) Let us assume that there is at least a cohort large enough for one such class of designers. Let us assume that one university is willing to make the required investment in developing such a program. What kinds of curriculum do we require if we are to educate such students at university? How many years will this take? What degrees will they earn?
(5) Conversely, let us assume the possibility that cohorts are too small to make attracting students possible. Or let us assume the possibility that such a program would be too expensive, even for an elite university. Is it possible that we might meet the need for mathematically fluent designers by simply allowing the right people to find there way into both fields?
There are in the world today such persons as Mark Burry, John Gero, Donella Meadows, or Don Norman who sometimes use fluent expressive mathematics of the kind Terry describes. This is a contrast with engineering design mathematics of the everyday kind in use at companies such as BMW, Microsoft, or nearly any telecom provider. The people who mastered mathematics to this level acquired these skills in different ways and brought them to the design field without the benefit of a dedicated program. If such individuals are rare, is it better to let them self-select than to prepare a costly program for which there may be too few applicants?
So far, no one has pointed to published working examples of design projects that require and use the kinds of mathematical fluency for which Terry argues. Not even Terry seems to do this kind of work. Once again, peer-reviewed publication is the difference between professional mathematics at the level of fluent mastery. Saying it could be done or should be done is speculation. Describing possible projects in imagined worlds is fiction. If there are no published examples of actual design projects demonstrating this level of mathematical skill, it is difficult to see why designers should learn to speak this particular language.
Investing 10,000 hours is a real commitment. There are two sets of costs.
One set of costs involves the investment in time required for expertise.
This also involves the investment in time required to teach and coach experts. Masters in every field generally require expert coaching to develop their skills.
But there is a second set of costs. Robert Sternberg's (1996) article, "Costs of Expertise," addresses this. In essence, it is the cost of skills and experience foregone by those who master a skill. To put it another way, there is a possibility that those who master mathematics at a high level of fluency will not have the time, mental, or emotional capacity to master design at a high level of fluency. I do not argue that this is the case, but I do argue that it is possible. In fact, I am willing to propose that a great many people involved in design and design research now do not invest the time, or lack the capacity to master design or design research. This accounts for a great deal of the attrition in our field - and it accounts for the great number of practitioners whose deficiencies render them mediocre or even incompetent.
Medical education and medical certification tend to weed out true incompetence, though mediocrity often gets through. This is also the case in engineering. There is no similar process in most design fields for most nations.
Given these problems, I'm really wondering where we are to find truly skilled designers who also demonstrate true capacity and skill for "mastering abstraction and meta-abstraction along with predicting dynamic behaviors in multi-dimensional spaces, going beyond linear four-dimensional understanding of the world, understanding and using limits and disjoints, moving between discrete and continuous, combinatorics and design theory (different from what is known as design theory in the design industry), understanding the calculus of change and feedback, and moving between set and metrological mapping of concepts" (Love 2014).
At different points, Birger Sevaldsen, Martin Salisbury, Francois Nsenga, and I have all asked Terry to address these issues. In each case, there has been no answer, but rather a period of silence followed by a new round of assertions on the importance of high-level mathematics to design practice.
In my last post (Friedman 2014), in Martin's (Salisbury 2014), and in Francois's (Nsenga 2014) opening and subsequent posts, we have raised questions that have gone unanswered.
If anyone can answer any of these five questions or all of them, I'd be interested to read the answers.
It could be that no one wishes to address these issues other than Terry. In that case, let silence reign.
Yours,
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
Guest Professor | College of Design and Innovation | Tongji University | Shanghai, China ||| Adjunct Professor | School of Creative Arts | James Cook University | Townsville, Australia
--
References
Colvin, Geoffrey. 2008. Talent is Overrated. What Really Separates World-Class Performers from Everybody Else. New York: Portfolio.
Coyle, Daniel. 2009. The Talent Code. Greatness Isn't Born. It's Made.
Here's How. New York: Bantam.
Ericsson, K. Anders, Ralf Th. Krampe, and Clemens Tesch-Romer. 1993. "The Role of Deliberate Practice in the Acquisition of Expert Performance."
Psychological Review, Vol. 100. No. 3, pp. 363-406.
Ericsson, K. Anders, and Neil Chamess. 1994. "Expert Performance. Its Structure and Acquisition." American Psychologist, Vol. 49, No. 8, pp.
725-747.
Ericsson, K. A., and A. C. Lehmann. 1996. "Expert and Exceptional Performance. Evidence of Maximal Adaptation to Task Constraints." Annual Review of Psychology, Vol. 47, pp. 273-305.
Ericsson, Karl Anders, ed. 1996. The Road to Excellence. The Acquisition of Expert Performance in the Arts and Sciences, Sports, and Games. Hillsdale,
NJ: Lawrence Erlbaum Associates, Inc.
Friedman, Ken. 2014. "Re: Maths, the language for everyone, including (fine) artists?" PhD-Design List. Monday 28 April, 2014.
Gladwell, Malcom. 2008. Outliers. The Story of Success. New York: Little, Brown, and Company.
Love, Terence. 2014. "Re: Maths, the language for everyone, including (fine) artists?" PhD-Design List. Friday 25 April, 2014.
Nsenga, Francois. 2014. "Maths, the language for everyone, including (fine) artists?" PhD-Design List. Wednesday 23 April, 2014.
Salisbury, Martin. 2014. "Re: Maths, the language for everyone, including
(fine) artists?" PhD-Design List. Monday 28 April, 2014.
Sternberg, Robert J. 1996. "Costs of Expertise." In: The Road to Excellence.
The Acquisition of Expert Performance in the Arts and Sciences, Sports, and Games. Karl Anders Ericsson, ed. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc, pp. 347-354.
Syed, Matthew. 2010. Bounce. How Champions are Made. London: Fourth Estate.
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