Without thinking about it, we tend to associate certain types of creative activities with certain media. We assume songs are created artistically, machines are engineered and brochures are designed.
This is not true at all. Not only are many supposed designs actually art — much of what is done in interaction design is a species of engineering. Entire genres of music have been designed (pop) or engineered (serial music). And some of what is thought of as pure engineering is actually art or design. (If German cars were only well-engineered, nobody would care about them.)
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Design is something beyond art and engineering. It is not a combination of the two, or even a higher synthesis.
Design involves a wholly different approach entirely outside of what happens in even the best art and the best engineering. Both art and engineering (and combinations of the two) can be done without reference to any other people than the creator and the creation. Design is always done in reference to third parties who are understood to perceive, conceive, feel and behave differently from the creator. A creator can attempt to design without direct involvement of users, but this means resorting to speculative design processes.
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If you are making a thing solely to please your own sensibility, you are making art.
If you are making a thing solely to function in some defined way, you are engineering.
If you are making a thing and involving the people who will be experiencing that thing and concerning yourself with their sensibilities and their functional needs, you are designing.