Dear Terry,

You wrote a post to the lost arguing that designers should master mathematics at a serious university level – this requires “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.”

At the end of your post, you write, “I’m interested in others’ thoughts on this.”

I’m willing to share my thoughts without defending them in a complete debate. I am still working to answer the questions you asked in an earlier thread, so this is an outline of my thoughts without further argument. As it is, responding carefully to your massive argument has taken 2,500 words and several days of work and thought. That’s all I can give it.

The article by Mariza Munah in the New Times makes a simple and true statement: mathematics is a useful tool in daily life. We’ve all got to buy food, pay bills, purchase clothing, and so on.

This is not university level mathematics, and this is not what you’ve been saying.

Nearly everyone agrees with Munah on the uses of math in daily life. You are speaking of a different and far higher level of mathematics.

While I agree that you have always described a different and higher level of mathematics, your larger point is more complex.

I do not agree that all designers or even most designers need the level of advanced mathematics for which you argue.

In different conversations, you have proposed mathematics as a universally applicable way of stating and working with design problems and theories.

As I understand it, you argue that mastering mathematics is a vital step for the entire design field and all design subfields. You do not limit your claim to high-level engineering. Rather, you argue that engineering has made great advances by using mathematics, and you argue that all design fields would advance significantly were they to follow suit.

The level of mathematics and the mathematical skill involved here is far greater than anything Munah proposes. The ability to use mathematics as an expressive language rather than an everyday tool requires fluency and mastery.

There are two problems here. One is conceptual. This other problem is practical.

Some mathematical applications work reasonably well at an everyday level. Others require fluent mastery. You have never explained why this high level of mathematical skill is useful for ALL designers in ALL design applications. If this is, indeed, what you are saying, I would like to know why this is so.

If I have misread you, and you do not argue that these skills are useful for ALL designers in ALL design applications, then it would be interesting to know WHICH designers need these skills, and why.

If any designers need these skills, a practical problem remains to be solved. Learning to use mathematics at the level of a fluent, expressive language takes study, learning, and practice. How are design schools to develop these skills within the ordinary curriculum in the time available for an ordinary design student?

Some time back, Francois asked you to propose a mathematics curriculum for designers. You have never done this. Without a reasonable proposal, even in draft form or outline form, no one who educates design students is likely to take your proposal seriously.

No design program today incorporates serious training in mathematics. This requires major curriculum changes in any design school known to me. Any major change to a degree program has resource implications and time implications. It requires a solid conceptual argument explaining why the curriculum should add courses that teach these skills. You haven’t explained why this should be the case for the high-level mathematics you advocate.

No university would consider a design program with the kind of mathematical requirements you propose on the basis of the argument you’ve made here.

You must also show that this kind of curriculum change is possible within available resources. To argue in a serious way that this level of mathematics is necessary for a robust design education, you’ve got to offer a serious curriculum plan and some kind of demonstration that it would be possible to implement this plan in the time available for a design education without neglecting other necessary skills.

My thoughts are these:

(1) First, I don’t see how these skills are as important as you claim. Expressive fluency in mathematics may be useful for some kinds of research and some kinds of professional design. I don’t see a clear demonstration for the larger claims you’ve made.

In the past, people have asked you for examples and arguments in conversations involving your assertions about mathematics. You do not provide them.

You have on occasion offered links to what you believe are good examples elsewhere. In my view, to make a good argument, you must state your own case with an argument here, where you make the claims.

(2) Second, without a clear explanation for the value of fluent, expressive mathematics, you seem to be substituting the claims of one design tradition for other traditions.

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 is not an argument for high-level engineering design; it is the basic form of argument underlying the artisan craft guild tradition. Artisans make the claim of mastery and they make the claim that everyone in their profession requires these specific skills. In this case, you are taking the role of master craftsman and you argue that all who enter the design professions require these skills.

I know why physicians and lawyers need most of the skills that they are required to master in professional school. I agree that professional design education does not teach all the skills designers require today.

Where we differ is with respect to mathematics. It does not seem to me that designers need the skills involved in the specific education you propose.

I’d like to know why you make this claim – and I’d like to see the full argument, either in a post to this list or in a specific article on why designers need these skills. If you haven’t written such an article, I’d be happy with such an article by any author at all.

That’s quite different to an article in which one researcher or another demonstrates their skill and knowledge in using mathematics. It is also different to an article on mathematics education demonstrating that there are different kinds, styles, and uses of mathematics.

As it is, I don’t see that the articles you posted support your case. These articles address different issues entirely. Paul Ernest’s (1999) article addresses mathematics education and the philosophy of mathematics. It is relevant to the rhetoric of mathematics, but not to whether designers or even design researchers have a general reason to use mathematical rhetoric at a high level of fluency.

John Gero’s (2011) article is also irrelevant to your claims. Gero is using advanced mathematics to address a specific problem in the psychology of design – this is a psychological article about design. Gero does not argue that designers require an advanced level of mathematical knowledge.

What you’ve never done in this thread or any other is to present a carefully reasoned argument for the value of high-level fluency in expressive mathematics in design education or the general design profession.

While I can see the use of expressive mathematics for mathematicians, I can’t see the value of fluent mathematics for all designers in all forms of design education.

(3) Third, there remains a practical problem that you have never addressed.

IF – for the sake of argument – IF it were the case that all designers, or any, are to achieve fluency, how will we educate them?

To achieve genuine mastery in university-level and post-graduate professional mathematics requires fundamental skills developed through years of study in primary and secondary school, then serious study and practice at university level.

You have repeatedly argued for a level of mathematical skill that may confer advantages in the practice of design or in design research without demonstrating in a convincing way that this is the case.

But IF this were so, you have not shown us how we are to educate designers to the level of skill that you assert they require, and you have not distinguished between the skills level required for design practice and the skills level required for design research.

My thought, therefore, is that Mariza Munah’s argument is simple yet true because Munah argues for everyday mathematics to the level that all citizens require in the modern world.

In contrast, my though is that your arguments are interesting, but problematic.

It is not clear that all designers require a high level of mathematical skill, or even most designers. Quite the contrary, those designers who work on the kinds of highly complex projects that require advanced mathematics generally work in interdisciplinary teams in which some team members have these skills.

In my view, the notion that all designers – or even most designers – needed fluency in the kinds of advanced mathematics you propose is much like the 19th century argument that a sound education required Latin. While mathematics is likely to be more useful than Latin in most professions, it is not the case that most professionals need the kinds of advanced mathematics for which you argue.

Most of us agree that professional design education must change.

It is not clear that this change requires “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.”

IF, however, all serious design education required this level of mathematical skill, we would have a real problem. This would require a far lengthier and more demanding education than we offer today. I would argue, in fact, that many practicing engineers get by without fluency in ALL these kinds of advanced mathematics.

I’d like to know why ALL designers require these skills or even why ANY do. Without an explanation, these assertions remain an imaginary ideal.

Since you’ve asked for my thoughts, I can explain it best with an analogy that came to mind: if we required all designers were to study medicine and specialize in thoracic surgery, all designers would be able to perform heart and lung operations. This would be true, yet irrelevant. That’s my thinking on designers “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.”

Let me be clear on five issues:

1) This is not an argument against advanced mathematics. Advanced mathematics discloses a great deal about the world, and it offers the potential to disclose a great deal more about our world and about our minds. There is serious work to be done in the study of computability and incomputability, mind and mathematics, complexity and emergence, and other fields. These require that people speak the language of mathematics at a fluent level. I support advanced mathematics. I simply don’t believe that most designers require this, nor even most researchers in the design fields.

2) This is not an argument against SOME people in design practice or design research mastering and using fluent mathematics. Surely there is room for these. Several of the best designers known to me are expert in different fields of mathematics, computation, and statistics. These, however, are rare individuals who have mastered BOTH the language of mathematics AND the professional practice of design. This includes some engineers, but I observe that most engineers are better at designing for machines than designing for people. Engineers who design for machines may speak fluent mathematics, but they speak only one narrow design dialect, and I do not count them as fluent designers. So I’d argue that this group of engineering designers are the specific group of designers to which you belong, and not the broad range of all designers for whom you advocate advanced mathematical fluency.

3) Finally, your argument requires an explicit justification in the form of a well crafted statement in human, rhetorical terms of WHY all designers require this education. That can’t be stated in mathematical terms. It requires the language of human goals. So far, you have not made this clear. To my knowledge, no one has done so, except, perhaps, in the same kind of normative logic that demands Latin as the foundation of a good education.

4) IF anyone can demonstrate that all designers or even any group of designers broad enough to justify a curriculum track, THEN it would be necessary to show how this can be done. First, there is the problem of locating the entry cohort of students. Then, it would be necessary to demonstrate the resources and outcome of an education that will likely require two or three years of specific university-level study.

In comparison, I’ll point to an education that requires a high level of mathematical skill without the level of mathematics you propose: product design engineering. There are thirty or so product design engineering programs in the world. Of these, about half a dozen graduate fully qualified designers who are also fully certified engineers. The remaining programs tend to be hybrids, not as comprehensive, and without the nearly total employability of the half dozen programs.

If the world’s 18,000 or so universities only support half a dozen such programs with immediate industry application and nearly total graduate employability, I find it hard to imagine where or how we can develop the kinds of mathematical fluency you argue for.

5) Finally, as always, I’d even be interested in actual working examples of design projects that require and use the kinds of mathematical fluency for which you argue. I’m not talking about mathematical projects or social research projects or physics projects, and I’m not talking about statistical research in all the fields that use it – I’m asking for PUBLISHED design projects and design research projects.

If we are indeed talking about fluent mathematics, published projects mean peer-reviewed publications. It can also take the form of monographs from a high-level scientific publisher that uses expert review to vet books for mathematical quality. That’s the standard to which professional mathematicians subscribe, and that is the demonstration of fluent mathematics.

Without examples, it is difficult to demonstrate the merits of your argument.

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

Ernest, Paul. 1999. “Forms of Knowledge in Mathematics and Mathematics Education: Philosophical and Rhetorical Perspectives.” Educational Studies in Mathematics. Volume 38, Issue 1-3, March 1999, pp. 67-83. DOI 10.1023/A:1003577024357

Gero, John S. 2011. “Fixation and Commitment While Designing and its Measurement.” The Journal of Creative Behavior. Vol. 45, No. 2, June 2011, pp. 108–115. DOI: 10.1002/j.2162-6057.2011.tb01090.x

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Terry Love wrote:

—snip—

I feel it’s important, however, when talking about the role of maths in creative activities such as designing, we get the levels right.

For example, in talking about the use of creative writing in design and advertising copywriting we have in mind a level of competence and learning about understanding language and its competence in use. Its insufficient to have ‘cat sat on the mat’ level of reading and writing. A higher level of education is expected and needed. Competence in the use of language would be expected to be of the level of university, understanding the different aspects of rhetoric, syntax, grammar, tropes, as well as professional variants on AIDA etc.

Similarly is the level of competencies for the use of mathematics in design. Much of the useful mathematics for creative activity and design is university level rather than school level. Crucial seems to be is mastering abstraction and meta-abstraction along with predicting dynamic behaviours 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.

I’m interested in others’ thoughts on this.

—snip—




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