Dear Terry,
Well, I must be several cards short of a deck. Or perhaps you have not explained it s l o w l y enough.
First, you keep moving back and forth between different kinds of mathematics.
You started with the demand that all design students study university-level mathematics to be able to work with mathematics as fluent, expressive language. Mathematicians and physicists use that kind of mathematics, and it is well above rocket science.
Then you shifted to a kind of workaday high-school algebra mathematics. That’s the kind Lubomir talked about when he stated that he must have misunderstood your call for high-level expressive mathematics.
At some points you seem to be talking about engineering mathematics. Now this is not expressive, but this is, in fact, rocket science mathematics. It’s the kind of mathematics that engineers use when they build a rocket or launch a spacecraft.
On several occasions, we’ve been in a border zone. You say that we’re talking about simple arithmetic and algebra, but the kinds of problems you propose solving require higher levels of mathematical fluency.
I won’t quote your original statement on what designers should be able to do mathematically or quote the passage that went too fast for Gunnar – and evidently for me. These descriptions appear in enough posts for any list member to find them.
The grounds of your argument shift, the basis of your claims changes from post to post, but the answer is always that all design students should learn mathematics.
It seems that your argument is that for human designers to have an advantage over computers, they must be able to do better than computers what computers do well. With the claim of representing and manipulating abstractions of abstractions, you can see why a simple fellow such as myself went wrong on the amounts of data involved.
Your answers remain evasive on the main issues. In the world you claim is rushing toward us, computers will design. Most design users do not need high-end design services today.
There is nearly no mathematics in most design education today.
You argue, variously, for a design curriculum that graduates high-end designers who are skilled at one of three kinds of mathematics.
(1) One is high-level, fluent mathematical language for expressive representation and manipulation. This is the level of mathematics required for mathematics, physics, and for research and practice in the exact sciences as well as for rigorous research in some of the behavioural sciences, including some forms of experimental psychology and economics.
(2) The second is high-level mathematics at the level of manipulating data successfully. The is the kind of mathematics that engineers use, along with working chemists, some forms of financial engineering and accountancy, and – well, rocket science. Researchers also use this kind of mathematics for statistics in all fields, as well as for research in other branches of the behavioural sciences, including some forms of experimental psychology and economics.
(3) The third is workaday arithmetic and algebra. Now I can’t see how you can do the kind of mathematics you call for with only arithmetic and algebra, but that’s probably because I am so poorly equipped for serious debate.
Adding this to the curriculum would be an expensive process that will only be justified with a clear, understandable argument.
This brings us back to a few simple questions. The first is why? You still haven’t answered that question.
The second is how design students are to learn this. Your earlier answer was that today’s design teachers should take professional development courses to become mathematics teachers at the proper moments. Your proposal was that these design teachers should insert little mathematics lessons into every design course rather like downloading an app for an iPhone.
To do this well, people would have to learn enough mathematics so that they would, in North American terms, have a design major and a mathematics minor. But we’re not talking about new university students. We are talking about graduated designers who have worked a different way for many years.
As you have often explained to the PhD-Design list, design teachers today are generally incompetent in mathematics and uncomfortable working with mathematics. This is correct. People who are incompetent in a subject in which they are uncomfortable do not teach it well. So I’d be curious how this is to be done in an affordable way.
But I understand that I’m already asking the wrong questions. Oh dear, indeed. If only you knew how difficult it is to be perpetually mistaken as I surely am. A clear explanation would surely help.
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
—snip—
Oh dear, Ken
No. Ken, you are mistaken. I was writing bout maths in everyday design situations, not large datasets, though it can also be used in that way. The kind of use of maths I described depends on an ability to be able to flow to and fro between the concrete world and abstract accurate-enough structures that can predict. It doesn't need difficult maths - though you can go there if you want. Currently, designers do that flow with other kinds of abstract representations. Adding maths is just an extra dimension to that.
Gunnar is closer to the mark in his understanding.
An example, working out the best layout for an interface that will present information of different types at many different resolutions and screen sizes and has to work well for all of them and for old and young alike. A traditional design way is to make some images of different kinds of layouts and then try and work out (perhaps using lots of discussion and stakeholder collaboration) which ones work and fail and perhaps understand why at least a little and then revise with lots of cycles through the process creating more and more images until eventually finding something that might work - ish.
Alternatively, one can represent what is known about screen layouts, readability, information distribution, usability, ergonomics etc in simple math. Then, imagine absolutely ALL the possible images that could be creatively invented using the traditional design approach. Think of this as the solution search space. Somewhere in all those zillions of possible images is the few that will work, and somewhere in that group are the ones that offer optimal designs. Now, see the simple maths above as a way of slicing away all the parts of the solution space in which solutions are unsatisfactory. What is left is a maths representation of a space of solutions with the best designs. Typically the maths is simple arithmetic and algebra - just repurposed and applied to design. Often it can be done using simple sketches of abstract phenomena. This is simple abstraction if design knowledge processed in and out of maths, it's not mathematical rocket science.
—snip—
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