Dear Terry,

While your reply to my post restates your views, you have not made any kind of effort to answer the five questions.

The book chapter on functional costing is an example of relatively simple functional mathematics. Since all designers cost products and services, I’m willing to concede that this skill might be useful to most designers – though not, perhaps, vital to anyone with someone in a consultancy, firm, or design team who handles the costings.

Your Guidelines for Design Thinking (Love 2010) apply specifically to your own kind of design practice. This is a unique and narrow slice of design practice.

My post on Monday (Friedman 2014a) addressed what I see as a problem in these guidelines: “As I see it, you are making claims for your own specific tradition of engineering design. But you are not making the claim that this level of mathematics is solely for high-level engineering design. You are arguing for mathematics as the foundation of all design. … You have explained what sorts of skills fluent mathematics can enable, but you haven’t explained why most designers need these skills. … It seems to me that you are essentially saying, ‘Design would work better if everyone were able to work as I [Terry Love] work.’ ”

This thread grew from your claim that designers require high-level mathematical fluency, not workaday costings mathematics. You describe this high-level fluency (Love 2014) as 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.”

Francois Nsenga, Martin Salisbury, and I have all asked you specific questions. You haven't answered our questions, but merely restated your original point in different ways. Once again, you’ve offered a specific example of a workaday mathematical tool at a far lower level than the fluent, expressive language of mathematics that you described. Then you pointed us to your own guidelines. These do not make an argument for the mathematics you describe. They are a statement of your approach to design. These are not guidelines for design thinking – they are guidelines for those who want to solve problems in the way that one designer thinks. These guidelines work best for quantized problems in engineering design and machine systems.

Your guidelines miss a specific aspect of design thinking: working with people to solve human problems. The literature of design thinking emphasizes iterative problem-solving with stakeholder interaction and rapid prototyping. Your guidelines offer a normative problem-solving heuristic for quantized problems. The value of an iterative approach with stakeholder interaction and rapid prototyping is that you move repeatedly closer to solving the real problem while learning about the virtues and faults of different solutions. The problem of quantized engineering solutions to human problems is that you can reach correct mathematical answers without solving human problems.

In comparison, George Polya’s (1973 [1957]) How to Solve It offers a far richer and more robust set of heuristics for problem solving. Many of Polya’s rubrics apply to solving problems for people. Polya was a working mathematician and a professor of mathematics at Stanford University. He wrote this book for mathematicians and mathematics students. Even so, these are thinking tools, and Polya’s propositions work well for many kinds of problems, including problems that human beings can solve without using mathematical tools. In contrast, your guidelines are specifically mathematical and specifically require mathematics. To see the difference compare Love (2010) with Polya’s (1973 [1957]: xi-xv) rubrics.

For those who have not read Polya, I have posted a PDF copy to my Academia page in the “Teaching Documents” section:

https://swinburne.academia.edu/KenFriedman

This document will remain available through Monday, 6 May.

You have not yet answered any of the five questions I asked. Both Chuck Burnette and Eduardo Corte-Real have answered them: if the answer to the first question is that designers do not need these skills, there is no need to answer the remainder.

While I tend to agree with Chuck and Eduardo, I’m of the view that a few practicing designers may need these skills – very few, very few indeed, but a few. Some percentage of researchers in different design fields may also need mastery of fluent, expressive mathematics beyond the level of research statistics that most should have, but these are also few in proportion to the entire field of design research.

You are arguing for something more. You have stated that all designers will benefit from high-level fluency (Love 2014) in mathematical language, defined as 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.”

Thus I ask you 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?

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

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References

Friedman, Ken. 2014a. “Re: Maths, the language for everyone, including (fine) artists?” PhD-Design List. Monday, 28 April 2014.

Love, Terence. 2014. “Re: Maths, the language for everyone, including (fine) artists?” PhD-Design List. Friday 25 April, 2014.

Love, T. 2010. Guidelines for Design Thinking. Love Design and Research. URL: http://www.love.com.au/index.php/thoughts/20-guidelines-for-design-thinking
Date accessed 2014 May 4.

Polya, G. 1973 [1957]. How to Solve It. A New Aspect of Mathematical Method. Second edition. Princeton, New Jersey: Princeton University Press.

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