Dear all,
My first 2 years at the university of Stockholm was spent studying theoretical maths (not the same as engineering math, which is practical. Our professor in calculus even ordered us to tear out a page on "the practical use of calculus") And here are my 2 pennies:
1) Rock, paper and scissors - Maths are the whole world, not.
Maths is a not single thing, there are many, conflicting maths. Each is built on a set of assumptions. (called axoims)
At school you're most often taught a math called Euclidean geometry (probably what has been referred to as "simple math" in the thread). One axioms is that:
If A is larger than B, and
B is larger than C,
then A is larger than C. (transitivity)
This most often makes sense. 5 is larger than 4, 4 is larger than 3 and hey! 5 is larger than 3. But try it on rock. paper and scissors:
Rock is larger than scissors
Scissors is larger than paper
Then rock should be larger than paper, right?
The whole point of the game is the lack of "transitivity". If the world was actually Euclidean, the game couldn't exist. So the Euclidean geometry does not exactly model the real world, but is still useful. (There is still no math that is generally accepted to model everything in universe. Some math can even be used to argue that such math couldn't exist. Yikes.)
Another example is the computer iOs game Monument, which is based on Escher like figures that actually move and work. Try build that with wooden blocks!
Prof Bo Dahlbom once asked "If you make an exact simulation of weather, shouldn't it then rain inside the computer???"
So if you want to propose a maths curriculum you do need to work out which maths you want, but also what to leave out. And to remember that is not the world itself.
2) Adobe Illustrator - the calculus machine
Maths is today an intrinsic part of design tools, sure, at least the computer based. Take the example of Adobe Illustrator:
When you draw in Illustrator the computer samples the pen's position at different times. It the uses the data to generate an equation that graphically resembles what you've drawn. Then this equation can be used to generate your drawing at different resolutions. When you change the anchor points you are in fact changing elements of the equation. Most of you have noticed that often your indicated line changes when you lift the pen. That's because the equation is not exactly what you draw, just a model. First you draw, then the computer draws its mathematical interpretation of your drawing, which is little bit different. (The equations could be B-splines).
This is not just Illustrator, if you use Photoshop and a apply a Gaussian blur, that is also a mathematical operation. (Even named after a math guy).
Anything in a computer is represented as number and equations; movies, music, drawing... Granted.
3) But who cares?
Adobe people and others who design design-tools do need to pay a lot of attention, no doubt about it.
But why should anyone else? My colleague Lotta, who is an illustrator, wouldn't draw *better* if you knew the equations. In fact, if they had been a mandatory part of her training at Beckmans school of design she would have dropped out, or perhaps never even applied.
I think that most designers learn more from each other about the settings in Illustrator and Photoshop to achieve different results, than they would by staring at the equations. (Which are probably also a trade secret of Adobe.) Maybe a math skilled designer could come up with a better guide to Illustrator, to help illustrators produce the drawing they want. But not by listing all the equations in there.
In fact some math would tell you it is impossible to mathematically predict all the achievable effects, so the creativity is sometimes in spite of the intentions of the tool maker. If you had "known" the system you wouldn't have tried it.
Another funny example: A while ago architecture students at NYIT i NYC helped us design things for Gällivare/Kiruna. Unfortunately some renderings crashed, because the system couldn't generate shadows in places above the arctic circle, where the sun doesn't set in the summer and never rise in the winter.
All people are using loads of tools each day that few of us could explain in detail. A great ability (and a great source of anxiety) of modern people is using highly abstracted tools.
So there may be room for maths for certain, interested designers and certainly for those who build design tools. No doubt there are also a few designers with great skills in maths.
But as a requisite I think it would mostly be rather disastrous to the field, by excluding lots of talented people and limting their imagination.
Best Regards,
Lars
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LARS ALBINSSON
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9 maj 2014 kl. 08:27 skrev Ken Friedman <[log in to unmask]>:
Dear Terry,
Thanks for your note. I understand what you can do with the example you gave of linear programming and the related skills. I also see how engineers can use this for problems like traffic flow, logistics, operations management, and the like.
What I still don’t see is why ALL designers need to know this.
There are many examples of successful design projects that do not rely on mathematics for effective solutions. IDEO, Helsinki Design Lab, Aalto Design Factory, MindLab, DesignGov, and many others work in a completely different way. These groups of designers do well without mathematics. When they need advanced mathematical skills, they put the appropriate specialist on a team.
Nearly no fashion designer, textile designer, shoe designer, glass designer, or book illustrator needs abstraction, and certainly not the second-order abstraction of abstractions – they work in the world of material and form. Graphic designers may use computers, but they generally don’t need to model solution spaces. The same is true for those who work in advertising
This brings me back to my original question.
I understand what kinds of problems call for these different kinds of mathematical skills. I don’t why ALL designers need these skills.
I keep asking a question that you say is misguided. You believe that the very question predicates a specific answer. It seems to me that there is a satisfactory answer that would suit you, but you’ve got to give it. The answer would state: “All designers must learn mathematics [specify kind] to [specify skills] for [specify reason]”. This would obviously have to involve coverage of all design disciplines. I do not see why answering this question predicates an answer that suits me and not you. I would have been quite satisfied with a reasonable answer to the question that is without exception among all design fields. If you provide an answer that requires assent on logic and empirical data, I will assent.
As it is, there seems to be no way for me to ask the question in a way that you find satisfactory. Therefore, there is no way for me to address this problem.
It seems to me best to withdraw from the conversation on mathematics for designers. I will put my notes on this thread and the related threads aside. I’ll leave this to Martin, Gunnar, Lubomir, Eduardo and the others.
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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