This is my brain on Informatics and alcohol
A man once said that there is more information in a walk in the woods than there is available on your computer screen. That man was dead on.
Embedded environments will replace the traditional computer and embedded computing is going to change the way we sense our environment.
Connectivity will be the sixth sense. The value of a physical space will be calculated by its connectedness to the digital ether and sensors. New topographies will be created based on digital sensation.
Now constant connectivity to sensors is a huge shift in communication. Once there was only oral communication that depended on interactive human experience. Then there was written communication that depended on disembodied human experience. Now there is sensorial communication that conveys volumes of information without any human intermediation.
And it will be always on. You will be able to experience the life of a tree over years just by listening to the sensors. And it will always be on. What will happen when you can sense the present and the past, and predict the future to startling accuracy? What is a map when it is not a line on a piece of paper, but a video of what your trip will be?
Mapping physical and temporal space onto embedded or sensorial or computational space will drive all of the great shifts in interfaces in the next twenty years.
Mathematics is useful at finding patterns in life and studying its theory lets you see the patterns. You do not have to understand the patterns to use them. I am slightly drunk. So I understand only what I wrote on my arm.