Anthropomorphism is the propensity people have to attribute human
qualities to animals and objects
For example, people sometimes talk to their computers as if they were humans, treat their robot cleaners as if they were their pets, and give all manner of cute names to their mobile devices, routers, and so on.
Interaction Design, beyond human-computer interaction, 3rd Edition, Rogers, Sharp, Preece
In computing, a natural user interface, or NUI, is the common parlance used by designers and developers of computer interfaces to refer to a user interface that is effectively invisible, or becomes invisible with successive learned interactions, to its users. The word natural is used because most computer interfaces use artificial control devices whose operation has to be learned. A NUI relies on a user being able to quickly transition from novice to expert.
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I don’t believe there is any relevancy or relationship between anthropomorphism and NUI. Certainly not in multi-touch surfaces. Yes, you are using your hands and gesturing on touch interface, but is this really humanised? In my opinion touching a glass screen to interact with something is pretty inhuman and unnatural. Our hands are capable of so much more, we can grasp, clasp and feel all manner of textures.
Since the idea of anthropomorphism gives a connotation of humanistic
personalities, would designers' process of humanising natural user
interfaces in some way achieving partial anthropomorphism?
Because NUI is about the invisible aspects of the interface, or those that become invisible over time with successive learned interactions, the way you would achieve anthropomorphism would be if artificial intelligence could learn how a user interacts with an interface, makes those interactions more bespoke to the user, so that they can become more expert in their usage, but also increase the propensity for that user to attribute human qualities to it. For instance, if it were a voice interface, it may start out very synthetic and computerised. As it learns how the user interacts with it, it can become less synthetic and more human in how it responds to and perceives commands.
Going back to your main focus on multi-touch interfaces. I can’t see how anthropomorphism can be applied to this.